Question

An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.

Answer 1

Let common difference be d.

a = 3

Sum of first n terms of an A.P. = `n/2(a + 1)`

Given,

The sum of the first 8 terms is twice the sum of the first 5 terms.

∴ `8/2(a + a_8) = 2 xx 5/2(a + a_5)`

⇒ 4[a + a + (8 − 1)d] = 5[a + a + (5 − 1)d]

⇒ 4[2a + 7d] = 5[2a + 4d]

⇒ 4[2 × 3 + 7d] = 5[2 × 3 + 4d]

⇒ 4[6 + 7d] = 5[6 + 4d]

⇒ 24 + 28d = 30 + 20d

⇒ 28d − 20d = 30 − 24

⇒ 8d = 6

⇒ d = `6/8`

⇒ d = `3/4`