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(A) Let the first term of the first $AP$ be $a_1 = -1$ and the first term of the second $AP$ be $a_2 = -8$.Let the common difference for both $AP$s be

Vedclass · Accepted Answer

$7$

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(A) Let the first term of the first $AP$ be $a_1 = -1$ and the first term of the second $AP$ be $a_2 = -8$.Let the common difference for both $AP$s be $d$.The $n^{	ext{th}}$ term of an $AP$ is given by $T_n = a + (n - 1)d$.The $4^{	ext{th}}$ term of the first $AP$ is $T_4 = a_1 + (4 - 1)d = -1 + 3d$.The $4^{	ext{th}}$ term of the second $AP$ is $T'_4 = a_2 + (4 - 1)d = -8 + 3d$.The difference between their $4^{	ext{th}}$ terms is $(a_1 + 3d) - (a_2 + 3d) = a_1 - a_2$.Substituting the values,we get $(-1) - (-8) = -1 + 8 = 7$.Thus,the difference between their $4^{	ext{th}}$ terms is $7$.

Two $AP$s 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

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