Quiz Discussion

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]

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

(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

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

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

• 1]

  3

• 2]

  4

• 3]

  1

• 4]

  2

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

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]

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

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

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

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

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