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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

Sagot :

Answer:

B

Step-by-step explanation:

The sum to n terms of a geometric series is

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

where a is the first term and r the common ratio

Here a = 6144 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{3072}{6144}[/tex] = [tex]\frac{1}{2}[/tex] , then

[tex]S_{10}[/tex] = [tex]\frac{6144(1-(\frac{1}{2}) ^{10}) }{1-\frac{1}{2} }[/tex]

     = [tex]\frac{6144(1-\frac{1}{1024}) }{\frac{1}{2} }[/tex]

     = 12288(1 - [tex]\frac{1}{1024}[/tex] ) ← distribute

     = 12288 - 12

     = 12276 → B

toolboxj10

Answer:

B. 12,276

Step-by-step explanation:

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