Question

Find the missing terms of the AP: ___ , 3, ___ , -5.

Answer 1

Let the common difference for this AP be $d.$

Given that the $2^{\text{nd}}$ term in this AP is 3, and the $4^{\text{th}}$ term is -5.
i.e., $a_2=3$ and $a_4=-5$

Since $a_3=a_2+d$ and $a_4=a_3+d,$ we have
$a_4=a_3+d=(a_2+d)+d=a_2+2d.$
$⟹-5=3+2d$
$⟹d=-4$

$a_2=a_1+d$
$⟹a_1=a_2-d=3-(-4)=7$
Thus, the $1^{\text{st}}$ term of the AP is 7.

$a_4=a_3+d$
$⟹a_3=a_4-d=-5-(-4)=-1$
Thus, the $3^{\text{rd}}$ term of the AP is -1.