Question

The nth term of an AP is 5n+2. Find the common difference

Answer 1

Step-by-step explanation:

Given :-

$a_n = 5n + 2$

Putting, n = 1

$a_1 = 5(1) + 2$

$a_1 = 5 + 2$

$\boxed{a_1 = 7} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dashleftarrow(1)$

Putting, n = 2

$a_2 = 5(2) + 2$

$a_2 = 10 + 2$

$\boxed{a_2 = 12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dashleftarrow(2)$

Putting, n = 3

$a_3 = 5(3) + 2$

$a_3 = 15 + 2$

$\boxed{a_3 = 17} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dashleftarrow(3)$

Putting ,n = 4

$a_4 = 5(4) + 2$

$a_4 = 20 + 2$

$\boxed{a_4 = 22} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dashleftarrow(4)$

Now,

$common \: \: difference ,d_1= a_2 - a_1 = 12 - 7$

$\boxed{d_1 = 5}$

$d_2 = a_ 3 - a_2$

$d_2 = 17 - 12$

$\boxed{d_2 = 5}$

Hence the common difference is 5.

Therefore Ap will be ,

a,a+d,a+2(d),a+3(d).........

7, 7+5, 7+2(5), 7+3(5).....

7, 12, 17, 22......