The sum of the first n terms of an AP is (Gn + 6n). Find thethe 15th t

1.	The sum of the first n terms of an AP is (Gn + 6n). Find thethe 15th term of this AP.tem andCBSE 2014
Answer» Given,Sn = 3n² + 6n Put n = 1S₁ = 3(1)² + 6(1) = 3 + 6 = 9 Put n = 2S₂ = 3(2)² + 6(2) = 12 + 12 = 24 First term,a = S1 = 9Second term,a₂ = S₂ - S₁ = 24 - 9 = 15 Common difference,d = a₂ - a = 15 - 9 = 6 nth term,an = a + (n - 1)d = 9 + (n - 1)6 = 9 + 6n - 6 = 3 + 6n 15th term,a₁₅ = 3 + 6(15) = 3 + 80 = 83 nth term = 6n + 315th term = 83

The sum of the first n terms of an AP is (Gn + 6n). Find thethe 15th term of this AP.tem andCBSE 2014

Answer»

Given,Sn = 3n² + 6n

Put n = 1S₁ = 3(1)² + 6(1) = 3 + 6 = 9

Put n = 2S₂ = 3(2)² + 6(2) = 12 + 12 = 24

First term,a = S1 = 9Second term,a₂ = S₂ - S₁ = 24 - 9 = 15

Common difference,d = a₂ - a = 15 - 9 = 6

nth term,an = a + (n - 1)d = 9 + (n - 1)6 = 9 + 6n - 6 = 3 + 6n

15th term,a₁₅ = 3 + 6(15) = 3 + 80 = 83

nth term = 6n + 315th term = 83