Question

Let \( a_1, a_2, a_3, \dots \) be terms on A.P. If \[ a_1 + a_2 + \dots + a_p = p^2, \, p \neq q, \, \text{then} \, a_q = \frac{p^2}{q^2} \] Then \( a_q \) equals:

• A. \( \frac{41}{11} \)
• B. \( \frac{7}{2} \)
• C. \( \frac{2}{7} \)
• D. \( \frac{11}{41} \)

Hint:

In an arithmetic progression, use the sum formula and the given relations to find specific terms in the sequence.

Answer 1

The Correct Option is D

Step 1: Analyze the given A.P. relation.
We are given the sum of terms in A.P. and a relationship between the terms. Using the properties of arithmetic progression, we can solve for \( a_q \) and find that \( a_q = \frac{11}{41} \).
Thus, the correct answer is (4).