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)`.

पर्याय

• 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.

Answer 1

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)`.