SOLUTION: Determine S6 for the geometric series with properties listed below A) a = 5 and r = 10, B) t4= 6, and t6= 24

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Question 412050: Determine S6 for the geometric series with properties listed below
A) a = 5 and r = 10,
B) t4= 6, and t6= 24
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Geometric Series

a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n-1%29

sum%28+a%5Bi%5D%2C+i=1%2C+infinity+%29 = a(1-r^n)/(1-r)

A) sum%28+a%5Bi%5D%2C+i=1%2C+6+%29 = 5(1-10^6)/(1-10) = 5 *-999999/-9 = 555,555

B) a[6]= a[1]r^5 = 24 and a[4] = a[1]r^3= 6 

     a[1] = 6/r^3    (6/r^3)r^5 = 24  r^2 = 4, r = 2 and a[1] = 6/8 = 3/4

sum%28+a%5Bi%5D%2C+i=1%2C+6+%29 = 3/4*(1-2^6)/-1 = 47.25