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horsena [70]
3 years ago
9

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

Mathematics
2 answers:
Sonja [21]3 years ago
4 0
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
Grace [21]3 years ago
3 0

Answer:

C) 65535.

Step-by-step 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) = \frac{a_{2}}{a_{1} }

r =  \frac{12}{3}.

r = 4.

Sum = a_{1} \frac{(1-r^{n})}{1-r}

Then,

S_{8} =  3 \frac{(1-4^{8})}{1-4}.

S_{8}  =  \frac{-196605}{-3}.

 S_{8}  = 65535.

Therefore, C) 65535.

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