Question #7a5dd

1 Answer
Taha Z.
Sep 14, 2017

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#

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