Question

The sum of 41 terms of an A.P. with middle term 40 is ______.

Options

• 820

• 1640

• 2460

• None of these

Answer 1

The sum of 41 terms of an A.P. with middle term 40 is 1640.

Explanation:

Since middle term = 40

`\implies` T₂₁ = 40

`\implies` a + 20d = 40   ...(1)

We know that,

`S_n = n/2[2a + (n - 1)d]`

∴ `S_41 = 41/2[2a + 40d]`

= `41/2 xx 2[a + 20d]`

= 41 × 40   ...[Using (1)]

= 1640