Question

Find each sum

$1+3+5+...+59$

Short answer

The solution is$S_{30}=900$

Step-by-step solution

Given information

$1+3+5+...+59$

Calculation

We have, $1+3+5+...+59$

So, $a_1=1,d=2,a_n=59$

Now use formula,

$$\begin{gathered} a_n=a_1+(n-1)d \\ \Rightarrow 59=1+(n-1)2 \\ \Rightarrow 59=1+2n-2 \\ \Rightarrow 2n=60 \\ \Rightarrow n=30 \end{gathered}$$

To find sum $S_{30}$

$$\begin{gathered} S_{30}=\frac{30}{2}(1+59) \\ =900 \end{gathered}$$