Question

The fourth term of an A.P. is 11. The sum of the fifth and seventh terms of the A.P. is 34. Find its common difference.

Answer 1

Let a and d be the first term and the common difference of the AP, respectively.

∴ n^th term of the AP, a_n  = a + (n − 1)d

Given:

$$a_4=11$$

$$\Rightarrow a+(4-1)d=11$$
$$\Rightarrow a+3d=11.....\left(1\right)$$

Also, $$a_5+a_7=34$$

$$\Rightarrow (a+4d)+(a+6d)=34$$

$$\Rightarrow 2a+10d=34$$

$$\Rightarrow a+5d=17.....\left(2\right)$$

Solving (1) and (2), we get
a = 2 and d = 3
Hence, the common difference of the AP is 3.