Chapter 12.2, Problem 44E

To determine

Calculate the partial sum $S_n$ of the arithmetic sequence having $a=3,d=2,n=12$ .

Answer to Problem 44E

The partial sum of the arithmetic sequence is $S_n=168$ .

Explanation of Solution

Given information:

It is given in the question that, $a=3,d=2,n=12$

Formula used:

  $S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$

Where,

  $\begin{array}{l}aisthe{1}^{st}term\\ nisthenumberofterm\\ disthecommondifference\end{array}$

Calculation:

Here, $a=3,d=2,n=12$

So, by putting the value of $a,d\&n$ in the formula $S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$

  $\begin{array}{l}{S}_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]\\ S_n=\frac{12}{2}\left[2*3+\left(12-1\right)2\right]\\ S_n=6\left[6+\left(11\right)2\right]\\ S_n=6\left[6+22\right]\\ S_n=6\left[28\right]\\ S_n=168\end{array}$