1f the sum of n terms of an A.P. is S_n = 3n² + 5n. Write its common difference.

Let a1, a2, a3…….. an be the given A.P

Given, sum of n terms = 3n² + 5n

S_n=3n² + 5n……….(1)

Putting n =1 in (1)

S_n= 3x1² + 5x1

= 3 + 5 = 8

Sum of first 1 terms = first term

first term = a = S₁ = 8

S_n = 3n² + 5n

Putting n= 2 in….. (1)

S₂= 3x 2² + 5x2

S₂= 22

Sum of first two terms = first term + second term

S₂= a₁ + a₂

S₂ – a₁ = a₂

a₂= 22 – 8 = 14

Thus a₁= 8, a₂ = 14

d= common difference = 14 – 8= 6