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 $a_3=a_2+d\text{and}{a}_2=a_1+d$

$\Rightarrow a_1=a_2-d$

Given, $a_2=3\text{and}{a}_4=-5$

$a_4=a_3+d=a_2+d+d=a_2+2d$

$\Rightarrow 3+2d=-5$
$\Rightarrow 2d=-8$
$\Rightarrow d=-4$

The first missing term is equal to $a_2-d=3-d$
$=3-(-4)=7$

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