Find the Sum of the Series 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, ${\displaystyle a_n=a_1+d(n-1)}$.

Arithmetic Sequence: ${\displaystyle d=2}$

This is the formula of an arithmetic sequence.

Substitute in the values of ${\displaystyle a_1=3}$ and ${\displaystyle d=2}$.

Subtract ${\displaystyle 2}$ from ${\displaystyle 3}$.

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

Multiply ${\displaystyle 2}$ by ${\displaystyle 4}$.

Add ${\displaystyle 8}$ and ${\displaystyle 1}$.

Replace the variables with the known values to find ${\displaystyle S_4}$.

Divide ${\displaystyle 4}$ by ${\displaystyle 2}$.

Add ${\displaystyle 3}$ and ${\displaystyle 9}$.

Multiply ${\displaystyle 2}$ by ${\displaystyle 12}$.