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Ad libitum [116K]
3 years ago
6

The second term in a geometric series is 10, and the seventh term is 10,240. Find the sum of the first six terms.

Mathematics
1 answer:
just olya [345]3 years ago
5 0

Answer:

The sum of the first 6 terms is 3,412.5.

Step-by-step explanation:

The second term of the geometric series is given by:

a_{2}=a_{1}*r

Where a1 is the first term and r is the common ratio. The seventh term can be written as a function of the second term as follows:

a_{7}=a_{1}*r^{6} \\a_{7}=a_{2}*r^{5} \\10,240 = 10*r^{5}\\r=\sqrt[5]{1024} \\r = 4

The sum of "n" terms of a geometric series is given by:

a_{1} = \frac{10}{4} = 2.5\\S_{n}=a_{1}(\frac{r^{n}-1 }{r-1})\\S_{6}=2.5(\frac{4^{6}-1 }{4-1})\\S_{6}=3,412.5

The sum of the first 6 terms is 3,412.5.

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