Question

the algebraic form of the sum of n terms of an arithmetic sequence is 3n2 + 5 n .what is the common difference ?​

Answer 1

`d = 6`

Explanation:

Given

`S_n = 3n^2 + 5n`

Required

Find d

First, find the sum of the first 1 term

`S_1 = 3 * 1^2 + 5 * 1`

`S_1 = 8`

The sum of the first 2 terms

`S_2 = 3 * 2^2 + 5 * 2`

`S_2 = 22`

Calculate the first term (a)

`a = S_1`

`a = 8`

Calculate the second term (T2)

`T_2 = S_2 - S_1`

`T_2 = 22 - 8`

`T_2 = 14`

The common difference is:

`d = T_2 - a`

`d = 14 - 8`

`d = 6`