Question

The first term in a geometric series is 64 and the common ratio is 0.75. Find the sum of the first 4 terms in the series.

Answer 1

195.25

Explanation:

Consider geometric series S(n) where initial term is a

So S(n)=a+ar^1+...ar^n

Factor out a

S(n)=a(1+r+r^2...+r^n)

Multiply by r

S(n)r=a(r+r^2+r^3...+r^n+r^n+1)

Subtract S(n) from S(n)r

Note that only 1 and rn^1 remain.

S(n)r-S(n)=a(r^n+1 -1)

Factor out S(n)

S(n)(r-1)=a(r^n+1 -1)

The formula now shows S(n)=a(r^n+1 -1)/(r-1)

Now use the formula for the problem