Question

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

Class 10 - Math - Arithmetic Progressions Page 99

Answer 1

a =10
d=10
so the next four terms
will be a+d ;a+ 2d ; a+3d ; a +4d

so 2nd term = a+2d = 10+2x10 =30
simililary find the 3rd ; 4th term by substituing the values of a and d in a+3d ; a+4d


For the rest of the sums just follow the same process you will get it

Answer 2

AP  ( Arithmetic progression).
 
A list of numbers a1 ,a2, a3  ………….. an is called an arithmetic progression , Is there exists a constant number ‘d’


a2= a1+d
a3= a2+d
a4= a3+d……..
an= an-1+d ………


Each of the numbers in the list is called a term .

An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.

This fixed  number is called the common difference( d ) of the AP.

General form of an AP.:
a, a+d, a+2d, a+3d…….

Here a is the first term and d is common difference.

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Solution:

(i) Given: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
 the series will be 10, 20, 30, 40, 50 …

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

(ii)Given: a = – 2, d = 0Let 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
 the series will be – 2, – 2, – 2, – 2 …
First four terms of this A.P. will be – 2, – 2, – 2 and – 2.

(iii) Given:a = 4, d = – 3Let 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
 the series will be 4, 1, – 2 – 5 …
First four terms of this A.P. will be 4, 1, – 2 and – 5.

(iv) Given:a = – 1, d = 1/2Let the series be a1, a2, a3, a4 …a1 = a = -1
a2 = a1 + d = -1 + 1/2 = -1/2
a3 = a2 + d = -1/2 + 1/2 = 0
a4 = a3 + d = 0 + 1/2 = 1/2
the series will be-1, -1/2, 0, 1/2
First four terms of this A.P. will be -1, -1/2, 0 and 1/2.

(v)Given: a = – 1.25, d = – 0.25Let 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
 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.---------------------------------------------------------------------------------------------------Hope this will help you...