# What is the sum of the geometric sequence 8, 16, 32?

The sum of the geometric sequence is 56.

To find the sum of any geometric sequence, you use the equation: ${S}_{n} = \frac{a \left({r}^{n} - 1\right)}{r - 1}$where:

a --> is the first term of the sequence; in this case "a" is 8.

r --> is the ratio (what each number is being multiplied by) between each number in the sequence; in this case, each term is being multiplied by 2.

n --> is the number of terms in the sequence; in this case, there are 3 terms.

Knowing the value of each variable, you can substitute the values into the equation as follows:

${S}_{n} = \frac{8 \left({2}^{3} - 1\right)}{2 - 1}$

Simplify and solve:

${S}_{n} = \frac{56}{1}$

Therefore, the sum of the sequence is 56! Hopefully you've understood this and hopefully I was of some help! :)