Question

The common difference of an Arithmatic Progression, whose $3^{rd}$ term is $5$ and $7^{th}$ term is $9$, is ...............

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

We know that

$n^{th}$ term of an AP ,$a_n=a+(n-1)d$

where $a=$First term, $d=$Common difference and $n=$Position of term.

Given $3^{rd}$ term is $5$ ,
$a_3=a+(3-1)d$
$\Rightarrow 5=a+2d$
$\Rightarrow a=5-2d$........$\left(1\right)$

Given $7^{th}$ term is $9$,
$a_7=a+(7-1)d$
$\Rightarrow 9=a+6d$
$\Rightarrow a=9-6d$ .......$\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$
$5-2d=9-6d$
$\Rightarrow 6d-2d=9-5$

$\Rightarrow 4d=4$
$\Rightarrow d=1$
So , common difference is $1$