Question

Find the ${12}^{th},{24}^{th}$ and $nth$ term of the A.P. given by $9,13,17,21,25,...$

Answer 1

We have, $a=$First term $=9$.

and, $d=$Common difference $=4$ $[\because 13-9=4,17-13=4,21-17=4etc.]$

We know that the $n^{th}$ term of an A.P. with first term $a$ and common difference $d$ is given by

$a_n=a+(n-1)d$

$\therefore a_{12}=a+(12-1)d=a+11d=9+11\times 4=53$

$a_{24}=a+(n-1)d=9+(n-1)\times 4=4n+5$

Thus, we have

$a_{12}=53,a_{24}=101$ and $a_n=4n+5$.