Choose the correct answer from the given four options : Two APs h… - Vidyadip

MCQ

Choose the correct answer from the given four options : Two $\text{APs}$ 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 $4^{th}$ terms is :

A
$-1.$
B
$-8$
✓
$7$
D
$-9$

✓

Answer

Correct option: C.

$7$

Let the common diference of two $AP$ s are $d_1$ and $d_2,$ respectively.
Bycondition, $d_1= d_2= d$
Let the first term of first $AP (a_1) = -1$
and the first term of second $AP (a_2) -8$
we know that, the $n^{th}$ term of an $AP, T_1= a + (n - 1)d$
$\therefore 4^{th}$ term of first $AP, T_4= a + (4 - 1)d = -1 + 3d$
and $4^{th}$ term of second $AP, T_4= a_2+ (4 - 1)d = -8 + 3d$
Now, the difference between there $4^{th}$ term is i.e.,
$[T_4- T'_4] = (-1 + 3d) - (-8 + 3d)$
$= -1 + 3d + 8 - 3d = 7$

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