Find the Sum of the First 6 Terms

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by ${\displaystyle 2}$ gives the next term. In other words, ${\displaystyle a_n=a_1{r}^{n-1}}$.

This is the form of a geometric sequence.

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

Multiply ${\displaystyle 2^{n-1}}$ by ${\displaystyle 1}$.

This is the formula to find the sum of the first ${\displaystyle n}$ terms of the geometric sequence. To evaluate it, find the values of ${\displaystyle r}$ and ${\displaystyle a_1}$.

Replace the variables with the known values to find ${\displaystyle S_7}$.

Multiply ${\displaystyle \frac{{\left(2\right)}^7-1}{2-1}}$ by ${\displaystyle 1}$.