Have given one interesting question from progressions. This question is from challenge quiz I. This is not that difficult, but as with all good questions, there is a formula-based method of solving this and there is a more straightforward intuitive way of solving them.

Question

Sum of first 12 terms of a GP is equal to the sum of the first 14 terms in the same GP. Sum of the first 17 terms is 92, what is the third term in the GP?

- 92
- -92
- 46
- 231

Correct Answer** :** 92. Correct Choice : (1)

Explanatory Answer

Sum of first 12 terms is equal to sum of first 14 terms.

Sum of first 14 terms = Sum of first 12 terms + 13^{th} term + 14^{th} term

=> 13^{th} term + 14^{th} term = 0

Let us assume 13^{th} term = k, common ratio = r. 14^{th} term will be kr.

k + kr = 0

k (1 + r) = 0

=> r = -1 as k cannot be zero

Common ratio = -1.

Now, if the first term of this GP is a, second term would be -a, third would be a and so on

The GP would be a, -a, a, -a, a, -a,…

Sum to even number of terms = 0

Sum to odd number of terms = a

Sum to 19 terms is 92 => a = 92

Third term = a = 92

————————————————————————-

2iim – CAT Classes, Correspondence material.

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