Question

If the arithmetic mean of the terms \(a, a + d, a + 2d, ..... a + (2n)d\) is 35 and the sum of the series is 735, then the value of \(n\) is:

• A. 6
• B. 7
• C. 8
• D. 10

Hint:

For an arithmetic progression, \(\text{AM} = \frac{\text{Sum}}{\text{Number of terms}}\). Use this relation to find unknown \(n\) when AM and sum are known.

Answer 1

The Correct Option is D

The sequence has \(2n + 1\) terms. Arithmetic mean (AM) is given by: \[ \text{AM} = \frac{\text{Sum}}{\text{Number of terms}} = 35 \] Sum \(S = 735\), so \[ \frac{735}{2n + 1} = 35 \implies 2n + 1 = \frac{735}{35} = 21 \] \[ \Rightarrow 2n = 20 \implies n = 10 \]