Question

Find the ${17}^{th}$ term of the A.P. $4,9,14,....$

Answer 1

The given arithmetic progression is $4,9,14,......$ where the first term is $a_1=4$, second term is $a_2=9$ and so on.

We find the common difference $d$ by subtracting the first term from the second term as shown below:

$d=a_2-a_1=9-4=5$

We know that the general term of an arithmetic progression with first term $a$ and common difference $d$ is $T_n=a+(n-1)d$

To find the $17$th term of the A.P, substitute $n=17,a=4$ and $d=5$ in $T_n=a+(n-1)d$ as follows:

$T_{17}=4+(17-1)5=4+(16\times 5)=4+80=84$

Hence, the $17$th term of the given A.P is $84$.