Question

Find the first term and the common difference of an AP, if the $3^{rd}$ term is $6$ and the ${17}^{th}$ term is $34$.

Answer 1

If $a$ is the first term and $d$ is the common difference, then $n^{th}$ term is given by $a_n=a+(n-1)d$

Since, $a_3=6$ & $a_{17}=34$

$\therefore a+2d=6$ ...(1)
$a+16d=34$ ...(2)
On subtracting equation (1) from equation (2), we get
$a+16d-a-2d=34-6$

$14d=28$

$\Rightarrow$ $d=2$
Substituting the value of $d$ in equation (1), we get

$a+2\left(2\right)=6$

$\Rightarrow a=6-4=2$

$\therefore$ $a=2$ and $d=2$.