Find the sum of first 5 terms of the series 11, 121, 1331,...Choices:- 177155 12321 24123 23232
Question
Find the sum of first 5 terms of the series 11, 121, 1331,...Choices:- 177155 12321 24123 23232
Solution
The given series is a geometric series where each term is 11 times the previous term.
The sum of the first n terms of a geometric series can be found using the formula:
S_n = a * (r^n - 1) / (r - 1)
where: S_n is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 11, r = 11, and n = 5.
Substituting these values into the formula gives:
S_5 = 11 * (11^5 - 1) / (11 - 1)
Solving this gives:
S_5 = 11 * (161051 - 1) / 10
S_5 = 11 * 161050 / 10
S_5 = 177155
So, the sum of the first 5 terms of the series is 177155. Therefore, the correct choice is 177155.
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