If the 2^nd terms of an AP is 13 and 5^th term is 25, what is its 7^th term?

As we know, nth term of an AP is

a_{n =} a + (n - 1)d

where a = first term

a_n is nth term

d is the common difference

a_{2 =} a + d = 13 …..(1)

a_{5 =} a + 4d = 25 ……(2)

Solving 1 and 2

From 1 we have

a = 13 - d

using this in 2, we have

13 - d + 4d = 25

13 + 3d = 25

3d = 12

d = 4

a = 13 - 4 = 9

a_{7 =} a + 6d

= 9 + 6(4)

= 9 + 24 = 33