Question

The sum of n terms of an ap is 3n^2+4n. Find its r th terms is

Answer 1

Answer:

According to question,

Sum of n terms of an AP is given by

$S_n = {3n}^{2} + 4n$

So,

$a_1 = s_1 = 3 + 4 = 7 \\ \\ a_2 = s_2 - s_1 = 20 - 7 \\ \\ = 13 \\ \\ a_3 = s_3 - s_2 = 39 - 20 \\ \\ = 19 \\ \\ a_4 = s_4 - s_3 = 64 - 39 \\ \\ = 25 \\ . \\ . \\ . \\ . \\ . \\ . \\ .$

Now,

AP will be 7, 13, 19, 25,...........

So,

1st term of the AP ,

a = 7

Common difference of the AP,

d = 6.

So,

rth term will be

$a_r = a + (r - 1)d \\ a_r = 7 + (r - 1)6 \\ a_r = 7 + 6r - 6 \\ a_r = 6r + 1$

So,

rth term will be 6r + 1.