Question

If nth term of an ap is 2n+1 find the sum of first n terms

Answer 1

Answer:

n² + 2n

Step-by-step explanation:

Given that,

a(n) = 2n + 1.

To find the first term (a) Substitute "1" at the place of "n".

a(1) = 2(1) + 1

a = 3.

a(2) = 2(2) + 1

a(2) = 5.

Hence, the sequence will be 3,5,7...

Here , d(common difference) = t(n) - t(n - 1)

d = t(2) - t(1)

d = 5 - 3

d = 2.

We know that, S(n) = n/2 [ 2a + (n - 1)d]

=> n/2 [ 2(3) + (n - 1)(2)]

=> n/2 [ 6 + 2n - 2]

=> n/2 ( 2n + 4)

=> n/2 [ 2(n + 2)]

=> n(n + 2)

S(n) = n² + 2n

Hence, the sum of first n terms is n² + 2n.