Question

Select the correct answer.

1-
What is the sum of the first 10 terms of this geometric series? Use
Sn=
6,144 + 3,072 + 1,536 + 768 + ...
OA. 11,520
OB
12,276
OC. 23,040
OD. 24,550

Answer 1

B. 12,276

Explanation:

Answer 2

B

Explanation:

The sum to n terms of a geometric series is

`S_(n)` =
`(a(1-r^(n)) )/(1-r)`

where a is the first term and r the common ratio

Here a = 6144 and r =
`(a_(2) )/(a_(1) )` =
`(3072)/(6144)` =
`(1)/(2)` , then

`S_(10)` =
`(6144(1-((1)/(2)) ^(10)) )/(1-(1)/(2) )`

=
`(6144(1-(1)/(1024)) )/((1)/(2) )`

= 12288(1 -
`(1)/(1024)` ) ← distribute

= 12288 - 12

= 12276 → B