# Arithmetic Progressions

#### Question 2:

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:

(i) *a* = 10,* d*
= 10

Let
the series be *a*_{1}, *a*_{2}, *a*_{3},
*a*_{4}, *a*_{5} …

*a*_{1
}= *a* = 10

*a*_{2}
= *a*_{1} + *d* = 10 + 10 = 20

*a*_{3}
= *a*_{2} + *d* = 20 + 10 = 30

*a*_{4}
= *a*_{3} + *d* = 30 + 10 = 40

*a*_{5}
= *a*_{4} + *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 *a*_{1}, *a*_{2}, *a*_{3},
*a*_{4} …

*a*_{1
}= *a* = −2

*a*_{2}
= *a*_{1} + *d* = − 2 + 0 = −2

*a*_{3}
= *a*_{2} + *d* = − 2 + 0 = −2

*a*_{4}
= *a*_{3} + *d* = − 2 + 0 = −2

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

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