Difference between revisions of "1950 AHSME Problems/Problem 5"
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== Problem== | == Problem== | ||
− | If five geometric means are inserted between <math>8</math> and <math>5832</math>, the fifth term in the | + | If five geometric means are inserted between <math>8</math> and <math>5832</math>, the fifth term in the geometric series: |
<math> \textbf{(A)}\ 648\qquad\textbf{(B)}\ 832\qquad\textbf{(C)}\ 1168\qquad\textbf{(D)}\ 1944\qquad\textbf{(E)}\ \text{None of these} </math> | <math> \textbf{(A)}\ 648\qquad\textbf{(B)}\ 832\qquad\textbf{(C)}\ 1168\qquad\textbf{(D)}\ 1944\qquad\textbf{(E)}\ \text{None of these} </math> |
Latest revision as of 19:50, 13 July 2014
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
All AHSME Problems and Solutions |
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