The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term

1.	The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.
Answer» S_n = 4n² + 2n First term, a = 4(1)² + 2(1) = 4 + 2 = 6 Sum of first two terms, S₂ = 4(2)² + 2(2) a + a + d = 16 + 4 6 + 6 + d = 20 d = 8 Now the n^th term, a_n = a + (n – 1) d = 6 + (n – 1) 8 = 6 + 8n – 8 = 8n - 2

The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.

Answer»

S_n = 4n² + 2n

First term, a = 4(1)² + 2(1) = 4 + 2 = 6

Sum of first two terms, S₂ = 4(2)² + 2(2)

a + a + d = 16 + 4

6 + 6 + d = 20

d = 8

Now the n^th term, a_n = a + (n – 1) d

= 6 + (n – 1) 8

= 6 + 8n – 8

= 8n - 2