Question

Find the common difference if $n^{th}$ term of an A.P. is 2n + 1.

Answer 1

Hint- In this particular type of question we have to use the given relation between the $n^{th}$ term and n to find any two successive terms of the AP. Then we need to subtract them to find the desired common difference.

Complete step-by-step answer:
$n^{th}$ term= 2n+1
Therefore,
1st term ( putting n = 1 ) = $2\times 1+1=3$
2nd term ( putting n = 2 ) = $2\times 2+1=5$
Common difference is difference of two successive terms of AP ( Second term - First term).
 d = 5-3 = 2

Note- Remember to recall the concept of common difference of an AP to solve such questions. Note that in this question the formula for $n^{th}$ term of an AP is not required as a direct relation between the $n^{th}$ term and n is given. The common difference could also be calculated by using any two successive terms other than 1 and 2.