Question

In the following APs, find the missing terms in the boxes:

`square, 38, square, square, square, -22`

Answer 1

53, 38, 23, 8, -7, -22 

Explanation:

For this A.P.,

a₂ = 38

a₆ = −22

We know that

a_n = a + (n − 1) d

a₂ = a + (2 − 1) d

38 = a + d (1)

a₆ = a + (6 − 1) d

−22 = a + 5d (2)

On subtracting equation (1) from (2), we obtain

− 22 − 38 = 4d

−60 = 4d

d = −15

a = a₂ − d = 38 − (−15) = 53

a₃ = a + 2d = 53 + 2 (−15) = 23

a₄ = a + 3d = 53 + 3 (−15) = 8

a₅ = a + 4d = 53 + 4 (−15) = −7

Therefore, the missing terms are 53, 23, 8, and −7 respectively.