Question

Determine the A.P. whose 3^rd term is 16 and the 7^th term exceeds the 5^th term by 12.

Answer 1

We have given a₃ = 16

a + (3 − 1)d = 16

a + 2d = 16(1)

a₇ − a₅ = 12

[a + (7 − 1)d] − [a + (5 − 1)d] = 12

(a + 6d) − (a + 4d) = 12

2d = 12

d = 6

From equation (1), we obtain

a + 2(6) = 16

a + 12 = 16

a = 4

Therefore, A.P. will be 4, 10, 16, 22, ...