Two A.P.s have the same common difference. The first term of one of these is $-1$ and that of the other is $-8$. Then find the difference between their $4^{th}$ terms.

Given: Two A.P.s have the same common difference. The first term of one of these is $-1$ and that of the other is $-8$. 

To do: To find the difference between their $4^{th}$ terms.

Solution:

Let $d$ be common difference of both A.P.

For $1^{st}$ A.P.-

First term, $a=-1$

$\therefore\ 4^{th}$ term, $a_4=a+( 4-1)d$

$a_4=-1+3d\ ..........\ ( i)$

For $2^{nd}$ A.P.-

First term, $a=-8$

Common difference$=d$

$\therefore\ 4^{th}$ term, $a_4=-8+( 4-1)d$

$\Rightarrow a_4=-8+3d\ ..........\ ( ii)$

Difference between the $4^{th}$ term of both A.P.$=-1+3d-( -8+3d)$

$=-1+3d+8-3d$

$=7$

Thus, the difference between the $4^{th}$ term of the both A.P. is $7$.

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Updated on: 10-Oct-2022

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