Question

If the sum of n terms of an A.P. is $S_{n} =3n^{2}+5n$. Write its common difference.

Answer 1

Answer:

The common Difference is 6 .

Step-by-step explanation:

Given :  

Sum of n terms = 3n² + 5n…….(1)

On putting n =1 in eq (1),

Sn = 3x1² + 5x1

S1 = 3 + 5  

S1 = 8

Sum of first 1 terms (S1) = first term(a) = 8  

 

On putting n = 2 in eq (1),

S2 = 3 x 2² + 5 x 2

S2 = 3 × 4 + 10

S2 = 12 + 10

S2 = 22

a2 = S2 - S1

[nth term of the A.P., an = Sn – S(n – 1)]

a2 = 22 - 8

a2 = 14

common difference , d = a2 - a1  

d = 14 - 8  

d = 6

Hence , the common Difference is 6 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Hi there!

Let a and d be the first term and common difference.

Sum of n terms = 3n² + 5n (Given)

When n=1

Sn = 3x1² + 5x1

S1 = 3 + 5  

S1 = 8

First term is 8 i.e (a=8)

When n = 2

S2 = 3 x 2² + 5 x 2

S2 = 3 × 4 + 10

S2 = 12 + 10

S2 = 22

a2 = S2 - S1

an = Sn – S(n – 1)

a2 = 22 - 8

a2 = 14

d= a2 - a1  

d = 14 - 8  

d = 6

Thankyou :)