Question

If nth term of AP is an+b then its common difference is

Answer 1

Please check the attachment

Answer 2

The common difference(d) = a.

Step-by-step explanation:

Given,

The nth term of AP, $a_{n}= an+b$

To find, the common difference(d) = ?

Put n = 1, 2, 3, 4...

First term,

$a_{1}= a(1)+b=a+b$

Second term,

$a_{2}= a(2)+b=2a+b$

Third term,

$a_{3}= a(3)+b=3a+b$

...

∴ Common difference(d) = Second term - First term = Third term - Second term

$=(2a+b)-(a+b)$

$=2a+b-a-b$

$=a$

Hence, the common difference(d) = a.