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

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

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

Answer»

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