Question

nth term of an ap is 5n+2. find the common difference

Answer 1

nth term of an ap is 5n+ 2

a1 = 5 × 1 + 2
a1 = 7

a2 = 12

a3 = 17

a4 = 22

a = 7

d = 12 - 7
d = 5.

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Answer 2

Given,

The nth term in the AP = 5n + 2

To Find,

The common difference(d) =?

Solution,

The nth term in the AP = 5n + 2

For the first term, putting n = 1

$a_1 = 5*1 + 2\\a_1 = 7$

For the second term of the AP, putting n = 2

$a_2 = 5*2 + 2\\a_2 = 10+ 2\\a_2 = 12$

Similarly, for the third term of the AP, putting n = 3

$a_3 = 5 * 3 + 2\\a_3 = 15 + 2\\a_3 = 17$

The AP is 7,12,17,22,......... up to nth term

The common difference(d) = $a_2 - a1$

The common difference(d) = 12 - 7

The common difference(d) =

Hence, if the nth term of an ap is 5n+2. then the common difference is 5.