Whats the missing term in the geometric sequence 2, __, 50?

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Whats the missing term in the geometric sequence 2, __, 50?

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Answer 1 · 2015-11-07T23:51:31

$10$ $10$

Explanation:

In a geometric sequence you multiply by some number $r$ $r$ to get to the next term. So if we call our missing term $x$ $x$ we know this:
$2 \cdot r = x$ $2*r = x$
$x \cdot r = 50$ $x * r = 50$

substitute...
$2 \cdot r \cdot r = 50$ $2*r *r = 50$

You could also think of each step in the sequence as multiplying by another $r$ $r$ , so basically your first term times $r$ $r$ and times $r$ $r$ again gives you 50. or $2 r^{2} = 50$ $2r^2 = 50$

Either way will get you there.
solve for r...
$2 r^{2} = 50$ $2r^2 = 50$
$r^{2} = 25$ $r^2 = 25$
$r = 5$ $r= 5$
Not done just yet...
plug in $r$ $r$ into one of the above equations...
$2 \cdot r = x$ $2*r = x$
$2 \cdot 5 = x$ $2*5 = x$
$10 = x$ $10 = x$

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Whats the missing term in the geometric sequence 2, __, 50?

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