Find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024 and select the correct answer below.

682
2,044
2,048
678

Question

Find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024 and select the correct answer below.

 682
 2,044
 2,048
 678

campbell_st · Answer

well you need to find the common ratio... 

you know the 9th term is 1024

and the 1st term is 4

so use the formula  for a term 

$$a_{n} = a_{1} \times r^{n - 1}$$

so 

$$1024 = 4\times r^8$$

solve for r. 

the fund the sum of 9 terms using 

$$S_{9} = \frac{4( 1 - r^9)}{1 - r}$$

hope it helps