Question

In an AP, given$l=28$, $S=144$ and there are total $9$ terms. find $a$.

Answer 1

Find the value of$a$

in an AP, given $l=28$, $S=144$ and $n=9$.

We know that, sum of the $n^{th}$ term is $S_n=\frac{n}{2}(a+l)$ where, $a$ is first term,$n$ is number of terms , $l$ is last term and $S_n$ is the sum of $n$ terms.

On substituting the given values in the above formula. we get,

$$\begin{gathered} \Rightarrow 144=\frac{9}{2}(a+28) \\ \Rightarrow 144=4.5(a+28) \\ \Rightarrow 144=4.5a+126 \\ \Rightarrow 4.5a=144-126 \\ \Rightarrow 4.5a=18 \\ \Rightarrow a=\frac{18}{4.5} \\ \Rightarrow a=4 \end{gathered}$$

Hence, the value of $a$ is $4$.