Find the nth term of the following sequence :
5 + 55 + 555 + . . . . Tn
5(10n - 1)
5n(10n - 1)
5/9×(10n−1)
(5/9)n×(10n−1)
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1
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(1) + (1 + 1) + (1 + 1 + 1) + ....... + (1 + 1 + 1 + ...... n - 1 times) = ......
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2
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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 \(\frac{{{S_1}}}{{{S_2}}}\)
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3
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The number of terms of the A.P. 3, 7, 11, 15, ....... to be taken so that the sum is 406 is
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4
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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
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5
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The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
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6
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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 = ?
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7
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What is the sum of the first 13 terms of an arithmetic progression if the first term is -10 and last term is 26?
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8
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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 :
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9
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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?
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10
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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
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