Question

The mean of numbers in A.P. 2, 4, 6, 8, …, 40 is ______.

Options

• `(40+2)/2`

• `20/2(2+40)`

• `10/2(2+40)`

• 840

Answer 1

The mean of numbers in A.P. 2, 4, 6, 8, …, 40 is `bbunderline((40+2)/2)`.

Explanation:

Given,

A.P. = 2, 4, 6, 8, ……, 40

First term (a) = 2

Common difference (d) = 4 − 2 = 2

Last term (l) = 40

Let no. of terms in A.P. be n.

⇒ 40 = a + (n − 1)d

⇒ 40 = 2 + 2(n − 1)

⇒ 40 = 2 + 2n − 2

⇒ 2n = 40

⇒ n = `40/2`​ = 20.

By formula,

Sum of first n terms of an A.P. = `n/2(a + l) = 20/2(2 + 40) = 420`

Mean = `"Sum of observations"/"No. of observations" = 420/20` = 21

Solving,

⇒ `(40+2)/2 = 42/2​ = 21`