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,
an=a+(n-1)d
an=a+(n-1)d
a6=a+(6-1)d
a6=a+5d
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,
an=a+(n-1)d
an=7+(n-1)4
an=7+(n-1)4
an=7+4n-4
an=3+4n
an=4n+3
an=4n+3
Hence, the required nth term of the AP is 4n+3.