1964 AHSME Problems/Problem 6
Problem
If are in geometric progression, the fourth term is:
Solution
Since we know the sequence is a geometric sequence, the ratio of consecutive terms is always the same number. Thus, we can set up an equation:
.
Solving it, we get:
or
If , the sequence has a as the second term, which is not allowed in a geometric sequence, so it is an extraneous solution that came about because we cross-multiplied by , which is .
If , we plug into to find the sequence starts as . The common ratio is . The next term is , which is option
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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