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 + 2d  ...(i)

And 9 = a + 6d  ...(ii)

Subtracting equation (i) from equation (ii),

(a + 6d) – (a + 2d) = 9 – 5

4d = 4

d = `4/4`

d = 1

Put d = 1 in equation (i),

5 = a + (2)1

5 = a + 2

a = 5 – 2

a = 3

So, the required A.P. is 3, 4, 5, 6, 7, 8, 9,....