Question

Question #7a5dd

Answer 1

63.9375

Explanation:

The formula of the geometric series (sum of n-terms of a pattern):
`S_n=(a(1-r^n))/(1-r)`
Where n is the number of terms, 10 in your case, and r is the common ratio.

The common ratio can be found by dividing any term from the term before:
`r=a_(n+1)/a_n`

Let us take any two terms and divide them:
`a_2/a_1=16/32=1/2`

Now that we have the common ratio`(1/2)` and the first term (32), we can calculate the sum.
`S_10=(32(1-(1/2)^10))/(1-(1/2))`

Simplifying:
`S_10=(32-32/2^10)/(1/2)`

Putting this in the calculator:
`S_10=(32-32/2^10)/(1/2)=63.9375`