Question

determine the ap whose 3rd term is 5 and the 7th term is 9?

Answer 1

3rd term = 5
a+2d = 5.......(1)
7th term = 9
a+6d = 9........(2)

(2) - (1)

a+6d=9
-(a+2d=5)
4d=4
d=4/4
d=1

put the value of d in equation (1)

a+2d=5
a+2(1)=5
a+2=5
a=5-2
a=3

a.p. series are:- 3,4,5,6,7,8,9,......

Answer 2

A3=5
A7=9
a+2d=5
a+6d=9
-4d=-4
d=1
a=3
ap is 3,4,5.......