Question

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

Answer 1

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= 3 x 2² + 5 x 2 

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