What is the sum of a 6–term geometric series if the first term is 24 and the last term is 1,417,176?
Answer Choices:
1,395,030

1,461,460

1,527,890

1,594,320

Question

What is the sum of a 6–term geometric series if the first term is 24 and the last term is 1,417,176? 
Answer Choices:
 1,395,030 

 1,461,460 

 1,527,890 

 1,594,320

amistre64 · Answer

the general setup is:$$a_1\frac{1-r^n}{1-r}$$

amistre64 · Answer

we know a1, and we know n, so the question is, what is r?

the general setup for a geometric sequence is:$$a_n=a_1~r^{n-1}$$
solving this for "r" we get:$$\Large \sqrt[n-1]{\frac{a_n}{a_1}}=r$$

anonymous · Answer

Not sure a sophisticated method is easier than brute force on this particular problem.  By using amistre64's formula above, we get r=9.  We can sum the powers of nine from zero to five, and multiply by 24 to get the solution.

anonymous · Answer

$$24\sum_{k=0}^{5}9^k=24[1+9+81+729+6561+59049]=1,594,320$$