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3 years ago

What is the sum of the first seven terms of the geometric series 2 - 10 +50 -...?

Mathematics

1 answer:

Umnica [9.8K]3 years ago

3 0

Answer:

26042.

Step-by-step explanation:

What's the first term of this geometric series?

What's the common ratio of this geometric series?

Divide one of the terms with the previous term. For example, divide the second term -10 with the first term 2.

$\displaystyle r = \frac{-10}{2} = -5$ .

What's the sum of this series to the seventh term?

The sum of the first n terms of a geometric series is:

$\displaystyle a_1 \cdot \frac{1-r^{n}}{1-r}$ ,

where

$a_1$ is the first term of the series,
$r$ is the common ratio of the series, and
$n$ is the number of terms in this series.

$\displaystyle 2 \times\frac{1- (-5)^{7}}{1- (-5)}=26,042$ .

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G cannot equal 5 and below because 12-5=7.

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The 2nd, 6th, 8th terms of an A.P. form a G.P. , find the common ratio and the general term of the G.P.

melisa1 [442]

The terms of an arithmetic progression, can form consecutive terms of a geometric progression.

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So, the <em>2nd, 6th and 8th terms </em>of the AP are:

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The <em>first, second and third terms </em>of the GP would be:

$\mathbf{a_1 = a + d}$

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$\mathbf{r = \frac{a_2}{a_1}}$

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Answer:

not telling u, imbecil

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