SOLUTION: First 4 numbers in a geometric series sums to 30, sum to infinity is 32. Find the first 2 numbers in the series. How do i even start on this :(

Question 1012957: First 4 numbers in a geometric series sums to 30, sum to infinity is 32. Find the first 2 numbers in the series.
How do i even start on this :(
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
sum of geometric series = a(1 - r^n) / (1 - r) where a is the first term, r is the common ratio and n is the number of terms to sum
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for the first part of our problem n=4
30 = a(1 - r^4) / (1 - r)
the second part gives us the sum for summing to infinity
let's try the sum to infinity formula that works for -1 < r < 1
sum = a / (1 - r)
32 = a / (1 - r)
solve for a
a = 32 * (1 - r)
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now substitute for a in our first equation
30 = 32 * (1 - r) * (1 - r^4) / (1 - r)
30 = 32 * (1 - r^4)
1 - r^4 = 30 / 32 = 15 / 16
r^4 = 1 / 16
r = + or - 1/2
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now use the infinity sum to get a
32 = a / (1 - 1/2)
a = 16
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the formula for the nth term of a geometric series is
An = Ao * r^(n-1)
we want the second term
A2 = 16 * (1/2)^(2-1)
A2 = 8
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The first two numbers in the series are 16, 8
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