What is the sum of an 8-term geometric series if the first term is 15 and the last term is -4,199,040?

Question

anonymous · Answer

so we know the general formula which is 

$$ar ^{n-1}$$ where a is the first term and r is the multiplier. We are doing a geometric series so forget the n-1. Just go with n. 

$$ar ^{1} = 15$$

We also know that the 8th term is 
$$ar ^{8} = -4, 199,040$$

we can find r .$$\frac{ r ^{8} }{ r } = \frac{ -4,199,040 }{ 15 }$$

solve for r and you get $$r ^{7} = -279,939$$

take the 7th root and you get -6 so r = -6.

Now to take the sum use the formula. $$Sn = a \frac{ [1-r ^{n}] }{[ 1-r]}$$

So now find the sum by substitution.