Question

Find the missing terms in the AP ___, 3,___, -5.

• A. 7, 1
• B. -7, 1
• C. 7, -1
• D. -7, 1

Answer 1

The correct option is C 7, -1

Let the common difference for this AP be d and the n${}^{th}$ term be $a_n$.

We know that the second term in this AP is 3 and the fourth term is -5.

We also know that
$a_3=a_2+d$ and $a_2=a_1+d$
$\Rightarrow a_1=a_2-d$
Given, $a_2=3$ and $a_4=-5$
$a_4=a_3+d=a_2+d+d=a_2+2d$
$\Rightarrow 3+2d=-5$
$\Rightarrow 2d=-8$
$\Rightarrow d=-4$
The first missing term is equal to $a_2-d=3-d$
$=3-(-4)=7$

The second missing term is equal to $a_2+d=3+d$
$=3+(-4)=-1$