1. For the following arithmetic progressions write the first term a and the common difference $d$: - Noon Academy

1. For the following arithmetic progressions write the first term a and the common difference $d$ :

Arithmetic Progression | Class 10 | ICSE | Maths | RD Sharma

1. For the following arithmetic progressions write the first term a and the common difference $d$ :

(i) $-5,-1,3,7,...$

(ii) ${1}/{5,{3}/{5}\;}\;,{5}/{5}\;,{7}/{5}\;,...$

An arithmetic progression is a number’s sequence such that the difference between the consecutive terms is constant.

Formula for this is: $an=d\left( n-1 \right)+c,$

Solution:

We know that if $a$ is the first term and $d$ is the common difference, the arithmetic progression is a, $a+d,a+2d+a+3d,....$

(i) $-5,-1,3,7,....$

Given arithmetic series is $-5,-1,3,7,...$

$c$ $a,a+d,a+2d+a+3d,....$

Thus, by comparing these two we get, $a=-5,a+d=1,a+2d=3,a+3d=7$

First term $\left( a \right)=-5$

By subtracting second and first term, we get

$\left( a+d \right)-\left( a \right)=d$

$-1-\left( -5 \right)=d$

$4=d$

$\Rightarrow$ Common difference $\left( d \right)=4$ .

(ii) $1/5,3/5,5/5,7/5,............$

Given arithmetic series is $1/5,3/5,5/5,7/5,...............$

It is seen that, it’s of the form of $1/5,2/5,5/5,7/5,...........a,a+d,a+2d,a+3d,$

Thus, by comparing these two, we get

$a=1/5,a+d=3/5,a+2d=5/5,a+3d=7/5$

First term $\left( a \right)=1/5$

By subtracting first term from second term, we get

$d=\left( a+d \right)-\left( a \right)$

$d=3/5-1/5$

$d=2/5$

$\Rightarrow$ common difference $\left( d \right)=2/5$

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