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

Posted by Vinayak Mishra 5 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 5 years, 10 months ago

We are to find the common difference of an A.P. if its n-th term is given by (an + b).

The n-th term of the A.P. is

{tex}a_n=an+b.{/tex}

Therefore, the (n+1)-th term of the A.P. will be

{tex}a_{n+1}=a(n+1)+b.{/tex}

We know that the common difference of an A.P. means the difference between two consecutive terms, so

{tex} {common difference},~d=a_{n+1}-a_n=(an+a+b)-(an+b)=a.{/tex}

Thus, the required common difference is 'a'.

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