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Nadusha1986 [10]
3 years ago
10

For the geometric series 2 + 6 + 18 + 54 + ... , find S8

Mathematics
2 answers:
dlinn [17]3 years ago
8 0

Answer:

\displaystyle S_{8}=6560

Step-by-step explanation:

We have the geometric sequence:

2, 6, 18, 54 ...

And we want to find S8, or the sum of the first eight terms.

The sum of a geometric series is given by:

\displaystyle S=\frac{a(r^n-1)}{r-1}

Where <em>n</em> is the number of terms, <em>a</em> is the first term, and <em>r</em> is the common ratio.

From our sequence, we can see that the first term <em>a</em> is 2.

The common ratio is 3 as each subsequent term is thrice the previous term.

And the number of terms <em>n</em> is 8.

Substitute:

\displaystyle S_8=\frac{2((3)^{8}-1)}{(3)-1}

And evaluate. Hence:

\displaystyle S_8=6560

The sum of the first eight terms is 6560.

marshall27 [118]3 years ago
4 0

Answer:

S₈ = 6560

Step-by-step explanation:

The sum to n terms of a geometric sequence is

S_{n} = \frac{a(r^{n}-1) }{r-1}

where a is the first term and r the common ratio

Here a = 2 and r = \frac{a_{2} }{a_{1} } = \frac{6}{2} = 3 , then

S₈ = \frac{2(3^{8}-1) }{3-1}

    = \frac{2(6561-1)}{2}

    = 6561 - 1

    = 6560

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