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Quantitative Aptitude - AP and GP - Formula & concept Quiz

# Quiz
1
Discuss
Formula & concept

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, the number of terms is

  • 1]

    10

  • 2]

    11

  • 3]

    12

  • 4]

    13

Solution
2
Discuss
Formula & concept

If the 7th term of a H.P. is 1/10 and the 12th term is 1/25, then the 20th term is

  • 1]

    1/41

  • 2]

    1/45

  • 3]

    1/49

  • 4]

    1/37

Solution
3
Discuss
Formula & concept

If three numbers be in G.P., then their logarithms will be in

  • 1]

    AP

  • 2]

    GP

  • 3]

    HP

  • 4]

     None Of This

Solution
4
Discuss
Formula & concept

If sum of n terms of an A.P. is 3n2 + 5n and Tm = 164 then m =

  • 1]

    26

  • 2]

    27

  • 3]

    28

  • 4]

    None Of This

Solution
5
Discuss
Formula & concept

The two geometric means between the number 1 and 64 are

  • 1]

    8 and 16

  • 2]

    2 and 16

  • 3]

    4 and 8

  • 4]

    4 and 16

Solution
6
Discuss
Formula & concept

If the sum of the series 2 + 5 + 8 + 11 … is 60100, then the number of terms are

  • 1]

    100

  • 2]

    150

  • 3]

    200

  • 4]

    250

Solution
7
Discuss
Formula & concept

Consider an infinite G.P. with first term a and common ratio r, its sum is 4 and the second term is 3/4, then

  • 1]

    a = 7/4, r = 3/7

  • 2]

    a = 2, r = 3/8

  • 3]

    a = 3, r = 1/4

  • 4]

    a = 3/2, r = ½

Solution
8
Discuss
Formula & concept

The sum of the first and third term of an arithmetic progression is 12 and the product of first and second term is 24, then first term is

  • 1]

    4

  • 2]

    1

  • 3]

    8

  • 4]

    6

Solution
9
Discuss
Formula & concept

If a, b, c are in A.P., then (a – c)2/ (b2 – ac) =

  • 1]

    3

  • 2]

    4

  • 3]

    1

  • 4]

    2

Solution
10
Discuss
Formula & concept

What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?

  • 1]

    897

  • 2]

    1,64,850

  • 3]

    1,64,749

  • 4]

    1,49,700

Solution
11
Discuss
Formula & concept

How many 2-digit positive integers are divisible by 4 or 9?

  • 1]

    32

  • 2]

    22

  • 3]

    34

  • 4]

    30

Solution
12
Discuss
Formula & concept

If log 2, log (2x -1) and log (2x + 3) are in A.P, then x is equal to ___

  • 1]

     

    5/2

  • 2]

    log25

  • 3]

    log32

  • 4]

     

    3/2

Solution
13
Discuss
Formula & concept

Find the nth term of the following sequence :
5 + 55 + 555 + . . . . Tn

  • 1]

     

    5(10n - 1) 

  • 2]

     

    5n(10n - 1)

  • 3]

    5/9×(10n−1)

       

  • 4]

    (5/9)n×(10n−1)

Solution
14
Discuss
Formula & concept

The 2nd and 8th term of an arithmetic progression are 17 and -1 respectively. What is the 14th term?

  • 1]

    -19

  • 2]

    -22

  • 3]

    -20

  • 4]

    -25

Solution
15
Discuss
Formula & concept

The 2nd and 6th term of an arithmetic progression are 8 and 20 respectively. What is the 20th term?

  • 1]

    56

  • 2]

    62

  • 3]

    65

  • 4]

    69

Solution
16
Discuss
Formula & concept

The first term of an Arithmetic Progression is 22 and the last term is -11. If the sum is 66, the number of terms in the sequence are:

  • 1]

    9

  • 2]

    10

  • 3]

    11

  • 4]

    12

Solution
17
Discuss
Formula & concept

What is the sum of the first 12 terms of an arithmetic progression if the first term is -19 and last term is 36?

  • 1]

    192

  • 2]

    230

  • 3]

    102

  • 4]

    204

Solution
18
Discuss
Formula & concept

The 3rd and 7th term of an arithmetic progression are -9 and 11 respectively. What is the 15th term?

  • 1]

    28

  • 2]

    87

  • 3]

    51

  • 4]

    17

Solution
19
Discuss
Formula & concept

What is the sum of the first 12 terms of an arithmetic progression if the 3rd term is -13 and the 6th term is -4?

  • 1]

    -30

  • 2]

    41

  • 3]

    -23

  • 4]

    -34

Solution
20
Discuss
Formula & concept

The sum of first five multiples of 3 is:

 

  • 1]

    90

  • 2]

    72

  • 3]

    55

  • 4]

    45

Solution
21
Discuss
Formula & concept

In an A.P., if d = -4, n = 7, an = 4, then a is

  • 1]

    6

  • 2]

    7

  • 3]

    20

  • 4]

    28

Solution
22
Discuss
Formula & concept

Which term of the A.P. 92, 88, 84, 80, ...... is 0?

  • 1]

    23

  • 2]

    32

  • 3]

    24

  • 4]

    28

Solution
23
Discuss
Formula & concept

If a + 1, 2a + 1, 4a - 1 are in A.P., then the value of a is:

 

  • 1]

    1

  • 2]

    2

  • 3]

    3

  • 4]

    4

Solution
24
Discuss
Formula & concept

If k, 2k – 1 and 2k + 1 are three consecutive terms of an AP, the value of k is

 

  • 1]

    -2

  • 2]

    -3

  • 3]

    2

  • 4]

    3

Solution
25
Discuss
Formula & concept

Let S denotes the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn – k Sn-1 + Sn-2 then k =

  • 1]

    1

  • 2]

    2

  • 3]

    3

  • 4]

    4

Solution
26
Discuss
Formula & concept

The number of terms of the A.P. 3, 7, 11, 15, ....... to be taken so that the sum is 406 is

  • 1]

    5

  • 2]

    10

  • 3]

    12

  • 4]

    14

Solution
27
Discuss
Formula & concept

How many terms are there in 20, 25, 30 . . . . . . 140?

  • 1] 22
  • 2] 25
  • 3] 23
  • 4] 24
Solution
28
Discuss
Formula & concept

Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

  • 1] 5
  • 2] 6
  • 3] 4
  • 4] 3
  • 5] 7
Solution
29
Discuss
Formula & concept

Find the 15th term of the sequence 20, 15, 10 . . . . .

  • 1] -45
  • 2] -55
  • 3] -50
  • 4] 0
Solution
30
Discuss
Formula & concept

The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is

  • 1] 600
  • 2] 765
  • 3] 640
  • 4] 680
  • 5] 690
Solution
31
Discuss
Formula & concept

How many terms are there in the GP 5, 20, 80, 320........... 20480?

  • 1] 5
  • 2] 6
  • 3] 8
  • 4] 9
  • 5] 7
Solution
32
Discuss
Formula & concept

A boy agrees to work at the rate of one rupee on the first day, two rupees on the second day, and four rupees on third day and so on. How much will the boy get if he started working on the 1st of February and finishes on the 20th of February?

  • 1] 220
  • 2] 220 -1
  • 3] 219 -1
  • 4] 219
  • 5] None of these
Solution
33
Discuss
Formula & concept

If the fifth term of a GP is 81 and first term is 16, what will be the 4th term of the GP?

  • 1] 36
  • 2] 18
  • 3] 54
  • 4] 24
  • 5] 27
Solution
34
Discuss
Formula & concept

The 7th and 21st terms of an AP are 6 and -22 respectively. Find the 26th term

  • 1] -34
  • 2] -32
  • 3] -12
  • 4] -10
  • 5] -16
Solution
35
Discuss
Formula & concept

After striking the floor, a rubber ball rebounds to 4/5th of the height from which it has fallen. Find the total distance that it travels before coming to rest if it has been gently dropped from a height of 120 metres.

  • 1] 540 m
  • 2] 960 m
  • 3] 1080 m
  • 4] 1020 m
  • 5] 1120 m
Solution
36
Discuss
Formula & concept

A bacteria gives birth to two new bacteria in each second and the life span of each bacteria is 5 seconds. The process of the reproduction is continuous until the death of the bacteria. initially there is one newly born bacteria at time t = 0, the find the total number of live bacteria just after 10 seconds :

  • 1]

    \(\frac{{{3^{10}}}}{2}\)

  • 2]

    310 - 210

  • 3]

    243 × (35 -1)

  • 4]

    310 - 25

  • 5]

    None of these

Solution
37
Discuss
Formula & concept

A square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely. If a side of the first square is 4 cm, determine the sum of the areas all the square.

  • 1] 32 Cm2
  • 2] 16 Cm2
  • 3] 20 Cm2
  • 4] 64 Cm2
  • 5] None of these
Solution
38
Discuss
Formula & concept

The first term of an Arithmetic Progression is 22 and the last term is -11. If the sum is 66, the number of terms in the sequence are:

  • 1] 10
  • 2] 12
  • 3] 9
  • 4] 8
Solution
39
Discuss
Formula & concept

Find the nth term of the following sequence :

  • 1]

    5(10n - 1)

  • 2]

    5n(10n - 1)

  • 3]

    \(\frac{5}{9} \times \left( {{{10}^n} - 1} \right)\)

  • 4]

    \({\left( {\frac{5}{9}} \right)^n} \times \left( {{{10}^n} - 1} \right)\)

Solution
40
Discuss
Formula & concept

The 2nd and 8th term of an arithmetic progression are 17 and -1 respectively. What is the 14th term?

  • 1] -22
  • 2] -25
  • 3] -19
  • 4] -28
Solution
41
Discuss
Formula & concept

The 2nd and 6th term of an arithmetic progression are 8 and 20 respectively. What is the 20th term?

  • 1] 56
  • 2] 65
  • 3] 59
  • 4] 62
Solution
42
Discuss
Formula & concept

What is the sum of the first 17 terms of an arithmetic progression if the first term is -20 and last term is 28?

  • 1] 68
  • 2] 156
  • 3] 142
  • 4] 242
Solution
43
Discuss
Formula & concept

The 4th and 7th term of an arithmetic progression are 11 and -4 respectively. What is the 15th term?

  • 1] -49
  • 2] -44
  • 3] -39
  • 4] -34
Solution
44
Discuss
Formula & concept

The 3rd and 8th term of an arithmetic progression are -13 and 2 respectively. What is the 14th term?

  • 1] 23
  • 2] 17
  • 3] 20
  • 4] 26
Solution
45
Discuss
Formula & concept

What is the sum of the first 11 terms of an arithmetic progression if the 3rd term is -1 and the 8th term is 19?

  • 1] 204
  • 2] 121
  • 3] 225
  • 4] 104
Solution
46
Discuss
Formula & concept

What is the sum of the first 13 terms of an arithmetic progression if the first term is -10 and last term is 26?

  • 1] 104
  • 2] 140
  • 3] 84
  • 4] 98
Solution
47
Discuss
Formula & concept

What is the sum of the first 12 terms of an arithmetic progression if the first term is -19 and last term is 36?

  • 1] 192
  • 2] 230
  • 3] 102
  • 4] 214
Solution
48
Discuss
Formula & concept

The 3rd and 7th term of an arithmetic progression are -9 and 11 respectively. What is the 15th term?

  • 1] 28
  • 2] 87
  • 3] 51
  • 4] 17
Solution
49
Discuss
Formula & concept

If the 3rd and the 5th term of an arithmetic progression are 13 and 21, what is the 13th term?

  • 1] 53
  • 2] 49
  • 3] 57
  • 4] 61
Solution
50
Discuss
Formula & concept

The 3rd and 6th term of an arithmetic progression are 13 and -5 respectively. What is the 11th term?

  • 1] -29
  • 2] -41
  • 3] -47
  • 4] -35
Solution
51
Discuss
Formula & concept

The 3rd and 9th term of an arithmetic progression are -8 and 10 respectively. What is the 16th term?

  • 1] 34
  • 2] 28
  • 3] 25
  • 4] 31
Solution
52
Discuss
Formula & concept

What is the sum of the first 9 terms of an arithmetic progression if the first term is 7 and last term is 55?

  • 1] 219
  • 2] 279
  • 3] 231
  • 4] 137
Solution
53
Discuss
Formula & concept

If 7 times the seventh term of an Arithmetic Progression (AP) is equal to 11 times its eleventh term, then the 18th term of the AP will be

  • 1] 0
  • 2] 1
  • 3] 2
  • 4] -1
Solution
54
Discuss
Formula & concept

The 7th and 12th term of an arithmetic progression are -15 and 5 respectively. What is the 16th term?

  • 1] 25
  • 2] 29
  • 3] 21
  • 4] 33
Solution
55
Discuss
Formula & concept

For an A.P. if a25 - a20 = 45, then d equals to:

  • 1] 9
  • 2] -9
  • 3] 18
  • 4] 23
Solution
56
Discuss
Formula & concept

For A.P. T18 - T8 = ........ ?

  • 1] d
  • 2] 10d
  • 3] 26d
  • 4] 2d
Solution
57
Discuss
Formula & concept

Which term of the A.P. 24, 21, 18, ............ is the first negative term?

  • 1] 8th
  • 2] 9th
  • 3] 10th
  • 4] 12th
Solution
58
Discuss
Formula & concept

15th term of A.P., x - 7, x - 2, x + 3, ........ is

  • 1] x + 63
  • 2] x + 73
  • 3] x + 83
  • 4] x + 53
Solution
59
Discuss
Formula & concept

If an A.P. has a = 1, tn = 20 and sn = 399, then value of n is :

  • 1] 20
  • 2] 32
  • 3] 38
  • 4] 40
Solution
60
Discuss
Formula & concept

The sum of first five multiples of 3 is:

  • 1] 45
  • 2] 65
  • 3] 75
  • 4] 90
Solution
61
Discuss
Formula & concept

(1) + (1 + 1) + (1 + 1 + 1) + ....... + (1 + 1 + 1 + ...... n - 1 times) = ......

  • 1]

    \(\frac{{n\left( {n + 1} \right)}}{2}\)

  • 2]

    \(\frac{{n\left( {n - 1} \right)}}{2}\)

  • 3]

    \({n^2}\)

  • 4]

    n

Solution
62
Discuss
Formula & concept

In an A.P., if d = -4, n = 7, an = 4, then a is

  • 1] 6
  • 2] 7
  • 3] 20
  • 4] 28
Solution
63
Discuss
Formula & concept

Which term of the A.P. 92, 88, 84, 80, ...... is 0?

  • 1] 23
  • 2] 32
  • 3] 22
  • 4] 24
Solution
64
Discuss
Formula & concept

If a + 1, 2a + 1, 4a - 1 are in A.P., then the value of a is:

  • 1] 1
  • 2] 2
  • 3] 3
  • 4] 4
Solution
65
Discuss
Formula & concept

A piece of equipment cost a certain factory 6,00,000. If it depreciates in value, 15% the first year, 13.5% the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost?

  • 1] Rs. 2,00,000
  • 2] Rs. 1,05,000
  • 3] Rs. 4,05,000
  • 4] Rs. 6,50,000
Solution
66
Discuss
Formula & concept

What is the sum of the following series? -64, -66, -68, ......, -100

  • 1] -1458
  • 2] -1558
  • 3] -1568
  • 4] -1664
Solution
67
Discuss
Formula & concept

What is the sum of all positive integers up to 1000, which are divisible by 5 and are not divisible by 2?

  • 1] 10,050
  • 2] 5050
  • 3] 5000
  • 4] 50,000
Solution
68
Discuss
Formula & concept

If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164 ?

  • 1] 26th
  • 2] 27th
  • 3] 28th
  • 4] None of these
Solution
69
Discuss
Formula & concept

The first and last term of an A.P. is a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \(\frac{{{l^2} - {a^2}}}{{k - \left( {l + a} \right)}}\)   then k = ?

 

  • 1] S
  • 2] 2S
  • 3] 3S
  • 4] None of these
Solution
70
Discuss
Formula & concept

If Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn , then S3n : Sn is equal to

  • 1] 4
  • 2] 6
  • 3] 8
  • 4] 10
Solution
71
Discuss
Formula & concept

Sum of n terms of the series \(\sqrt 2   +   \sqrt 8   +   \sqrt {18}   +   \sqrt {32}   +  \) ....... is

 

  • 1]

    \(\frac{{n\left( {n + 1} \right)}}{2}\)

  • 2]

    \(2n\left( {n + 1} \right)\)

  • 3]

    \(\frac{{n\left( {n + 1} \right)}}{{\sqrt 2 }}\)

  • 4]

    1

Solution
72
Discuss
Formula & concept

If the sums of n terms of two arithmetic progressions are in the ratio \(\frac{{3n + 5}}{{5n + 7}}\)   then their nth terms are in the ration

 

  • 1]

    \(\frac{{3n - 1}}{{5n - 1}}\)

  • 2]

    \(\frac{{3n + 1}}{{5n + 1}}\)

  • 3]

    \(\frac{{5n + 1}}{{3n + 1}}\)

  • 4]

    \(\frac{{5n - 1}}{{3n - 1}}\)

Solution
73
Discuss
Formula & concept

If 18, a, b - 3 are in A.P. then a + b =

  • 1] 19
  • 2] 7
  • 3] 11
  • 4] 15
Solution
74
Discuss
Formula & concept

If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio

  • 1] 3 : 2
  • 2] 3 : 1
  • 3] 1 : 3
  • 4] 2 : 3
Solution
75
Discuss
Formula & concept

If k, 2k – 1 and 2k + 1 are three consecutive terms of an AP, the value of k is

  • 1] -2
  • 2] 3
  • 3] -3
  • 4] 6
Solution
76
Discuss
Formula & concept

Two A.P.’s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th terms is

  • 1] 11
  • 2] 3
  • 3] 8
  • 4] 5
Solution
77
Discuss
Formula & concept

If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is

  • 1] n(n - 2)
  • 2] n(n + 2)
  • 3] n(n + 1)
  • 4] n(n - 1)
Solution
78
Discuss
Formula & concept

The common difference of the A.P. \(\frac{1}{{2b}} \frac{{1 - 6b}}{{2b}}  \frac{{1 - 12b}}{{2b}}\)   . . . . . is

 

  • 1] 2b
  • 2] -2b
  • 3] 3
  • 4] -3
Solution
79
Discuss
Formula & concept

If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6, then its first term is

  • 1] 2
  • 2] 3
  • 3] 1
  • 4] 4
Solution
80
Discuss
Formula & concept

If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are

  • 1] 5, 10, 15, 20
  • 2] 4, 10, 16, 22
  • 3] 3, 7, 11, 15
  • 4] None of these
Solution
81
Discuss
Formula & concept

If S1 is the sum of an arithmetic progression of ‘n’ odd number of terms and S2 is the sum of the terms of the series in odd places, then \(\frac{{{S_1}}}{{{S_2}}}\)

 

  • 1]

    \(\frac{{2n}}{{n + 1}}\)

  • 2]

    \(\frac{n}{{n + 1}}\)

  • 3]

    \(\frac{{n + 1}}{{2n}}\)

  • 4]

    \(\frac{{n - 1}}{n}\)

Solution
82
Discuss
Formula & concept

If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 term is

  • 1] 3200
  • 2] 1600
  • 3] 200
  • 4] 2800
Solution
83
Discuss
Formula & concept

The nth term of an A.P., the sum of whose n terms is Sn, is

  • 1] Sn + Sn - 1
  • 2] Sn - Sn - 1
  • 3] Sn + Sn + 1
  • 4] Sn - Sn + 1
Solution
84
Discuss
Formula & concept

The sum of first n odd natural numbers in

  • 1] 2n - 1
  • 2] 2n + 1
  • 3] n2
  • 4] n2 - 1
Solution
85
Discuss
Formula & concept

The sum of n terms of an A.P. is 3n2 + 5n, then 164 is its

  • 1] 24th term
  • 2] 27th term
  • 3] 26th term
  • 4] 25th term
Solution
86
Discuss
Formula & concept

The common difference of the A.P. \(\frac{1}{3}, \frac{{1 - 3b}}{3} , \frac{{1 - 6b}}{3}\)   . . . . . . is

 

  • 1]

    \(\frac{1}{3}\)

  • 2]

    \( - \frac{1}{3}\)

  • 3]

    -b

  • 4]

    b

Solution
87
Discuss
Formula & concept

If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of (p + q) terms will be

  • 1] 0
  • 2] p - q
  • 3] p + q
  • 4] -(p + q)
Solution
88
Discuss
Formula & concept

If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is :

  • 1] 13
  • 2] 9
  • 3] 21
  • 4] 17
Solution
# Quiz
Quantitative Aptitude

Quantitative Aptitude

  • Introduction
  • Number
    • Formula & Concept
  • AP and GP
    • Formula & concept
  • Problem On Ages
    • Formula & Concept
  • Percentages
    • Formulaes and Concept
  • Profit and Loss
    • Formula & Concept
  • Ratio & Proportions
    • Formula & Concepts
  • Time and work
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