Question

In the following APs find the missing term in the boxes

I.

II.

III.

IV.

V.

Answer 1

I.

For this A.P.,

a = 2

a₃ = 26

We know that, a_n = a + (n − 1) d

a₃ = 2 + (3 − 1) d

26 = 2 + 2d

24 = 2d

d = 12

a₂ = 2 + (2 − 1) 12

= 14

Therefore, 14 is the missing term.

II.

For this A.P.,

a₂ = 13 and

a₄ = 3

We know that, a_n = a + (n − 1) d

a₂ = a + (2 − 1) d

13 = a + d (I)

a₄ = a + (4 − 1) d

3 = a + 3d (II)

On subtracting (I) from (II), we obtain

−10 = 2d

d = −5

From equation (I), we obtain

13 = a + (−5)

a = 18

a₃ = 18 + (3 − 1) (−5)

= 18 + 2 (−5) = 18 − 10 = 8

Therefore, the missing terms are 18 and 8 respectively.

III.

For this A.P.,

We know that,

Therefore, the missing terms are and 8 respectively.

IV.

For this A.P.,

a = −4 and

a₆ = 6

We know that,

a_n = a + (n − 1) d

a₆ = a + (6 − 1) d

6 = − 4 + 5d

10 = 5d

d = 2

a₂ = a + d = − 4 + 2 = −2

a₃ = a + 2d = − 4 + 2 (2) = 0

a₄ = a + 3d = − 4 + 3 (2) = 2

a₅ = a + 4d = − 4 + 4 (2) = 4

Therefore, the missing terms are −2, 0, 2, and 4 respectively.

V.

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.