Question

Find each sum

$5+9+13+...+49$

Short answer

The solution is$S_{12}=324$

Step-by-step solution

Given information

$5+9+13+...+49$

Calculation

We have, $5+9+13+...+49$

So, $a_1=5,d=4,a_n=49$

Now use formula,

$$\begin{gathered} a_n=a_1+(n-1)d \\ \Rightarrow 49=5+(n-1)4 \\ \Rightarrow 49=5+4n-4 \\ \Rightarrow 4n=48 \\ \Rightarrow n=12 \end{gathered}$$

To find sum $S_{12}$

$$\begin{gathered} S_{12}=\frac{12}{2}(5+49) \\ =324 \end{gathered}$$