Question

Find the sum of the first 12 terms of the sequence 512, 256, 128, … This is infinite series notation, the answer is NOT 896...

Answer 1

1023.75

Explanation:

sum = a( 1 - r^n) / (1-r)

a1 = 512

n = 12

r = 256 / 512 = 1/2

512 (1 - 1/2¹²)

therefore.. sum = ------------------ = 1023.75

1 - 1/2

Answer 2

1023.75

Explanation:

The sum of a geometric sequence is

sum = a( 1 - r^n) / (1-r)

where a is the first term r is the common ratio and r^n is the nth term

We need to find the common ratio

r = 256/512 = 1/2

sum = 512 ( 1 - 1/2^12) / ( 1-1/2)

=512( 1-.000244141) / (.5)

=512(.999755859) /.5

=1023.75