Arithmetic Progressions Q?

Question

Determine the AP whose 3rd term is 5 and 7th term is 9.

Answer 1

We have

a3 = a + (3-1)d  = a +2d =5  ---------------------------------1)

a7 = a+ (7-1)d = a  + 6d ---------------------------------------2...

Solving the pair of inear equations 1) and 2) we get,

a = 3, d = 1

Hence the requires A.P. is 3, 4 5, 6, 7.....