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# Choose the correct answer from the given four options:

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

**(A)** $ -1 $

**(B)** $ -8 $

**(C)** 7

**(D)** $ -9 $

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:

We have 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 $4^{th}$ terms of both A.P.s $=-1+3d-( -8+3d)$

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

$=7$

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

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