Find the Sum of the Series 1+4+16+64+256+1024

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 ${\displaystyle 4}$ gives the next term. In other words, ${\displaystyle a_n=a_1\cdot r^{n-1}}$.

Geometric Sequence: ${\displaystyle r=4}$

This is the form of a geometric sequence.

Substitute in the values of ${\displaystyle a_1=1}$ and ${\displaystyle r=4}$.

Multiply ${\displaystyle {\left(4\right)}^{n-1}}$ 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 ${\displaystyle S_0}$.

Multiply ${\displaystyle \frac{{\left(4\right)}^0-1}{4-1}}$ by ${\displaystyle 1}$.

Convert the fraction to a decimal.