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What is the sum of the first seven terms of the geometric series? 3 12 48 192 ...

User Expurple
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1 Answer

4 votes

Answer:

16373

Explanation:

Pre-Solving

We are given the following geometric series:

3, 12, 48, 192....

And we want to find the sum of 7 terms.

The sum of n number of terms in a geometric series is
S_n=(t_1(1-r^n))/(1-r), where
t_1 is the first term, r is the common ratio, and n is the number of terms being added.

To get the common ratio, we can divide
(t_2)/(t_1); as we already know,
t_1 is the first term, which is 3.
t_2 is the second term, which is 12.

So, the common ratio is 12/3 = 4

Since we are finding the sum of the first seven terms, n = 7.

Solving

We can plug what we know into the formula.


S_n=(t_1(1-r^n))/(1-r)


S_7=(3(1-4^7))/(1-4)

Plug the above into a calculator.


S_7 = 16383

So, the sum is 16383.

User Kirk Sefchik
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