Question

Determine the A.P. whose third term is 5 and the seventh term is 9.

Answer 1

Given, T₃ = 5 and T₇ = 9

We know that the n^th term of an A.P. is

T_n = a + (n – 1)d

∴ 5 = a + 4d  ...(i)

And 9 = a + 6d  ...(ii)

Subtracting equation (i) from equation (ii),

–4 = –2d

⇒ d = 2

Put d = 2 in equation (i),

5 = a + 4(2)

⇒ a = 5 – 8

⇒ a = –3

So, the required A.P. is –3, –1, 1, 3, 5, 7, 9, .........