What is a possible value for the missing term of the geometric sequence 1250,__,50,..?

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What is a possible value for the missing term of the geometric sequence 1250,__,50,..?

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Answer 1 · 2017-01-04T00:37:25

$\pm 250$ $+-250$

Explanation:

The general term of a geometric sequence has the form:

$a_{n} = a \cdot r^{n - 1}$ $a_n = a*r^(n-1)$

where $a$ $a$ is the initial term and $r$ $r$ the common ratio.

In our example:

$a_{1} = 1250$ $a_1 = 1250" "$ and $a_{3} = 50$ $" "a_3 = 50$

So:

$r^{2} = \frac{a r^{2}}{a r^{0}} = \frac{a_{3}}{a_{1}} = \frac{50}{1250} = \frac{1}{25} = \frac{1}{5^{2}}$ $r^2 = (ar^2)/(ar^0) = a_3/a_1 = 50/1250 = 1/25 = 1/5^2$

Hence:

$r = \pm \frac{1}{5}$ $r = +-1/5$

Then:

$a_{2} = a \cdot r^{2 - 1} = 1250 \cdot (\pm \frac{1}{5}) = \pm 250$ $a_2 = a*r^(2-1) = 1250*(+-1/5) = +-250$

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What is a possible value for the missing term of the geometric sequence 1250,__,50,..?

1 Answer

Explanation:

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