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Question
Assertion: The sum of 5 terms of G.P. `2/9 - 1/3 + 1/2` ..... is `55/72`.
Reason: The sum of n terms of GP = `n/2(a + r)`.
Options
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
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Solution
Assertion (A) is true, but Reason (R) is false.
Explanation:
The Assertion (A) is true because the given sequence is a G.P. with first term a = `2/9` and common ratio r = `(-3)/2`. When you calculate the sum of 5 terms using the formula `S_n = (a(1 - r^n))/(1 - r)`, you get exactly `55/72`. However, the Reason (R) is false because it provides a completely incorrect formula; the sum of a G.P. is never calculated using `n/2(a + r)`.
