Question

the sum of 5th and 9th terms of an ap is72 and the sum of 7th and 12th termsis 97.find the ap.

Answer 1

Given
a5+a9=72
a+4d+a+8d = 72
2a+12d=72 ...(1)

and

a7+a12=97
a+6d+a+11d=97
2a+17d=97 ...(2)

(2)-(1),
5d=25
d=5

From (1),
2a+12(5)=72
2a+60=72
2a= 12
a=6.

So AP is
a, a+d, a+2d, a+3d,....
6, 11, 16, 21, 26,...