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.
A.682
B.2044
C.2048
D.678

Answer 1

First, we need to solve for the common ratio from the data given by using the equation.

a(n) = a(1) r^(n-1)
1024 = 4 r^(9-1)
256 = r^8
r = 256^(1/8)
r = 2

Then, we can find the sum by the expression:

S(n) = a(1) ( 1 - r^n) / 1-r
S(9) = 4 (1 - 2^9) / 1-2
S(9) = 2044

Therefore, the correct answer from the choices listed above is option B.