Find the nth term of an arithmetic progression whose . . .

Question : Find the nth term of an arithmetic progression whose first term is 7 and the 6th term of the AP exceeds its 2nd term by 16.

Doubt by Riddhi

Solution :

a = 7 (Given)

a₆-a₂=16

We know, 
a_n=a+(n-1)d

a₆=a+(6-1)d
a₆=a+5d

similarly 

a₂=a+d

a₆-a₂=16

a+5d-(a+d)=16

a+5d-a-d=16

a-a+5d-d=16

0+4d=16

4d=16

d=16/4

d=4

Now, 

a_n=a+(n-1)d
a_n=7+(n-1)4

a_n=7+4n-4

a_n=3+4n
a_n=4n+3

Hence, the required nth term of the AP is 4n+3.