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

1. 820

2. 1640

3. 2460

4. none of these

No. of terms = 41

Middle term = $\dfrac{41 + 1}{2} = \dfrac{42}{2}$ = 21st term

Given,

Middle term = 40

⇒ a₂₁ = 40

⇒ a + (21 - 1)d = 40

⇒ a + 20d = 40 …………(1)

By formula,

Sum of A.P. = $\dfrac{n}{2}$[2a + (n - 1)d]

= $\dfrac{41}{2}[2a + (41- 1)d]$

= $\dfrac{41}{2}[2a + 40d]$

= $\dfrac{41}{2} \times 2 \times [a + 20d]$

= 41 × 40 ……….[From (1)]

= 1640.

Hence, Option 2 is the correct option.