Question

if the sum of first n terms is 3nsquare+5n, then find its common difference

Answer 1

Hi...☺

Here is your answer...✌

Given that,

$S_{n} = 3 {n}^{2} + 5n \\ \\putting \: n = 1 \: \: we \: get\\ \\ \implies S_{1} = 3 {(1)}^{2} + 5(1) = 3 + 5 \\ \\ \implies S_{1} = 8 \\ \\ putting \: n = 2 \: \: we \: get \\ \\\implies S_{2} = 3 {(2)}^{2} + 5(2) = 12 + 10 \\ \\ \implies S_{2} = 22$

Now,

${ a}_{1} = S_{1} = 8 \\ \\ { a}_{2} = S_{2} - S_{1} = 22 - 8 = 14$

We know that,

Common difference , d = a2 - a1

d = 14 - 8

d = 6

Hence ,

The common difference is 6.

Answer 2

Hii friend,

Sn = 3n²+5n

Putting n = 1

S1 = 3×(1)² +5×1 = 8.

Putting n = 2

S3 = 3 × (2)² + 5 × 2 => 3×4+10 = 22.

First term (A) = S1 = 8

Second term = S2-S1 = 22-8 = 13

Common difference (D) = A2-A = 14-8 = 6

Hence,

Common difference is 6.

HOPE IT WILL HELP YOU..... :-)