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

Answer 1

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

Answer 2

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:\[\Large \sqrt[n-1]{\frac{a_n}{a_1}}=r\]

Answer 3

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.

Answer 4

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