Question

Question 11
Two APs have the same common difference. The first term of one of these is – 1 and that of the other is – 8. The difference between their $4^{th}$ terms is

A) -1
B) -8
C) 7
D) -9

Answer 1

Let the common difference of two APs be d.
The first term of first AP,
$a_1=-1$
The first term of second AP,
$b_1=-8$
We know that, the nth term of an AP,
$T_n$ = a + ( n – 1 ) d
$\therefore 4^{th}$ term of first AP,
$=a_1+(4-1)d=-1+3d$
$4^{th}$ term of second AP,
$=b_1+(4-1)d=-8+(4-1)d=-8+3d$
Now, the difference between their $4^{th}$ terms is i.e.,
$=(-1+3d)-(-8+3d)=-1+3d+8-3d=7$

Hence, the required difference is 7.