1950 AHSME Problems/Problem 5
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Problem
If five geometric means are inserted between and
, the fifth term in the gemetric series:
Solution
We can let the common ratio of the geometric sequence be .
is given to be the seventh term in the geometric sequence as there are five terms between it and
if we consider
.
By the formula for each term in a geometric sequence, we find that
or
We divide by eight to find:
Because will not be between
and
if
we can discard it as an extraneous solution. We find
and
See Also
1950 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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