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4 votes
What is the sum of the geometric sequence 3, 12, 48, ... if there are 8 terms?

A. 21,845
B. 43,690
C. 65,535
D. 87,380

2 Answers

1 vote

S_8=3+12+48+\cdots+12288+49152

S_8=3(4)^0+3(4)^1+3(4)^2+\cdots+3(4)^6+3(4)^7

4S_8=3(4)^1+3(4)^2+3(4)^3+\cdots+3(4)^7+3(4)^8


S_8-4S_8=-3S_8=3(4)^0-3(4)^8

-3S_8=3(1-4^8)

S_8=4^8-1

S_8=65535
User Euvl
by
7.1k points
1 vote

Answer:

C) 65535.

Explanation:

Given : sequence 3, 12, 48, ...if there are 8 terms.

To find : What is the sum of the geometric sequence.

Solution : We have given that 3, 12, 48, ......

We need to find 8th term of sequence.

Geometric ratio (r) =
(a_(2))/(a_(1) )

r =
(12)/(3).

r = 4.

Sum =
a_(1) ((1-r^(n)))/(1-r)

Then,


S_(8) =
3 ((1-4^(8)))/(1-4).


S_(8) =
(-196605)/(-3).


S_(8) = 65535.

Therefore, C) 65535.

User Vlaku
by
7.0k points