Q. 24.3( 226 Votes )

# Write first four terms of the AP, when the first term a and the common difference d aregiven as follows:

(i)

(ii)

(iii)

(iv)

(v)

Answer :

**(i)** Here, first term a_{1} = 10 and common difference, d = 10

Hence,

2^{nd} term a_{2} = a_{1} + d

= 10 + 10

= 20

3^{rd} term a_{3} = a_{1} + 2d

= 10 + 2 x 10

= 30

4^{th} term a_{4} = a_{1} + 3d

= 10 + 30

= 40

Therefore,

first four terms of the AP are:

10, 20, 30, 40, ……

**(ii)** Here,

First term a = -2 and Common difference = 0

Therefore, first four terms of the given AP are:

a_{1} = - 2, a_{2} = - 2, a_{3} = - 2 and a_{4} = - 2

**(iii)** Here, first term a_{1} = 4 and common difference d = - 3

We know that a_{n} = a + (n – 1)d, where n = number of terms

Thus, second term a_{2} = a + (2 – 1)d

a_{2} = 4 + (2-1)×(-3)

= 4 - 3 = 1

3^{rd} term a_{3} = a + (3 – 1)d

= 4 + (3-1) × (-3)

= 4 - 6

= -2

4^{th} term a_{4} = a + (4-1)d

= 4 + (4 - 1) ×( -3)

= 4 - 9 = -5

Therefore,

First four terms of given AP are:

4, 1, - 2, - 5

**(iv)** We have,

1^{st} term = - 1 and d = 1/2

Hence,

2^{nd} term a_{2} = a_{1} + d

= -1 + 1/2

= - 1/2

3^{rd}term a_{3} = a_{1} + 2d

= -1 + 2 * 1/2

= 0

4^{th} term a_{4} = a_{1} + 3d

= -1 + 3 * 1/2

= 1/2

Therefore,

The four terms of A.P. are -1, - 1/2, 0, 1/2

**(v)** We have

1^{st} term = - 1.25 and d = - 0.25

2^{nd} term a_{2} = a + d

= -1.25 - 0.25

= -1.5

3^{rd} term a_{3} = a + 2d

= -1.25 + 2 × (-0.25)

= -1.25 - 0.5

= -1.75

4^{th} term a_{4} = a + 3d

= -1.25 + 3 × (-0.25)

= -2

Therefore, first four terms of the A.P. are: -1.25, -1.5, -1.75 and – 2

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