Question

Write first four terms of the A.P. when the first term a and the common difference d are given as follows

(i) a = 10, d = 10

(ii) a = − 2, d = 0

(iii) a = 4, d = − 3

(iv) a = − 1 d =

(v) a = − 1.25, d = − 0.25

Answer 1

(i) a = 10, d = 10

Let the series be a₁, a₂, a₃, a₄, a₅ …

a₁ = a = 10

a₂ = a₁ + d = 10 + 10 = 20

a₃ = a₂ + d = 20 + 10 = 30

a₄ = a₃ + d = 30 + 10 = 40

a₅ = a₄ + d = 40 + 10 = 50

Therefore, the series will be 10, 20, 30, 40, 50 …

First four terms of this A.P. will be 10, 20, 30, and 40.

(ii) a = −2, d = 0

Let the series be a₁, a₂, a₃, a₄ …

a₁ = a = −2

a₂ = a₁ + d = − 2 + 0 = −2

a₃ = a₂ + d = − 2 + 0 = −2

a₄ = a₃ + d = − 2 + 0 = −2

Therefore, the series will be −2, −2, −2, −2 …

First four terms of this A.P. will be −2, −2, −2 and −2.

(iii) a = 4, d = −3

Let the series be a₁, a₂, a₃, a₄ …

a₁ = a = 4

a₂ = a₁ + d = 4 − 3 = 1

a₃ = a₂ + d = 1 − 3 = −2

a₄ = a₃ + d = − 2 − 3 = −5

Therefore, the series will be 4, 1, −2 −5 …

First four terms of this A.P. will be 4, 1, −2 and −5.

(iv) a = −1, d =

Let the series be a₁, a₂, a₃, a₄ …

Clearly, the series will be

………….

First four terms of this A.P. will be .

(v) a = −1.25, d = −0.25

Let the series be a₁, a₂, a₃, a₄ …

a₁ = a = −1.25

a₂ = a₁ + d = − 1.25 − 0.25 = −1.50

a₃ = a₂ + d = − 1.50 − 0.25 = −1.75

a₄ = a₃ + d = − 1.75 − 0.25 = −2.00

Clearly, the series will be 1.25, −1.50, −1.75, −2.00 ……..

First four terms of this A.P. will be −1.25, −1.50, −1.75 and −2.00.