1950 AHSME Problems/Problem 5
Problem
If five geometric means are inserted between and , the fifth term in the geometric 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 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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