What is the sum of an 8-term geometric sequence if the first term is 10 and the last term is
781,250? I know n=8, a1=10, an=781,250.
I just don't understand how to find the common ratio if a list of the terms is not given and the problem doesn't say what the common ratio is?

Question

What is the sum of an 8-term geometric sequence if the first term is 10 and the last term is 
781,250?	I know n=8, a1=10, an=781,250. 
I just don't understand how to find the common ratio if a list of the terms is not given and the problem doesn't say what the common ratio is?

campbell_st · Answer

then use the formula 

$$T _{n} = ar^{n-1}$$

to find the common ratio

$$781250 = 10r^{8-1}$$

$$r = \sqrt[7]{78125}$$

r = 5

next the sum of a geometric series is 

$$s _{n} = \frac{a( r^n -1)}{r-1}$$

substitute your values of n, a and r to find the sum.