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[tex]S_8=3+12+48+\cdots+12288+49152[/tex]
[tex]S_8=3(4)^0+3(4)^1+3(4)^2+\cdots+3(4)^6+3(4)^7[/tex]
[tex]4S_8=3(4)^1+3(4)^2+3(4)^3+\cdots+3(4)^7+3(4)^8[/tex]

[tex]S_8-4S_8=-3S_8=3(4)^0-3(4)^8[/tex]
[tex]-3S_8=3(1-4^8)[/tex]
[tex]S_8=4^8-1[/tex]
[tex]S_8=65535[/tex]

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) = [tex]\frac{a_{2}}{a_{1} }[/tex]

r =  [tex]\frac{12}{3}[/tex].

r = 4.

Sum = [tex]a_{1} \frac{(1-r^{n})}{1-r}[/tex]

Then,

[tex]S_{8}[/tex] =  [tex]3 \frac{(1-4^{8})}{1-4}[/tex].

[tex]S_{8}[/tex]  =  [tex]\frac{-196605}{-3}[/tex].

 [tex]S_{8}[/tex]  = 65535.

Therefore, C) 65535.

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