Find the Sum of the Series 1+3+5+7+9

This is the formula to find the sum of the first ${\displaystyle n}$ terms of the sequence. To evaluate it, the values of the first and ${\displaystyle n}$th terms must be found.

This is an arithmetic sequence since there is a common difference between each term. In this case, adding ${\displaystyle 2}$ to the previous term in the sequence gives the next term. In other words, ${\displaystyle a_n=a_1+d(n-1)}$.

This is the formula of an arithmetic sequence.

Substitute in the values of ${\displaystyle a_1=1}$ and ${\displaystyle d=2}$.

Subtract ${\displaystyle 2}$ from ${\displaystyle 1}$.

Substitute in the value of ${\displaystyle n}$ to find the ${\displaystyle n}$th term.

Multiply ${\displaystyle 2}$ by ${\displaystyle 5}$.

Subtract ${\displaystyle 1}$ from ${\displaystyle 10}$.

Replace the variables with the known values to find ${\displaystyle S_5}$.

Add ${\displaystyle 1}$ and ${\displaystyle 9}$.

Multiply ${\displaystyle 5}$ by ${\displaystyle 5}$.