1974 AHSME Problems/Problem 21: Difference between revisions
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[[Category:Introductory Algebra Problems]] | |||
Revision as of 09:20, 30 May 2012
Problem
In a geometric series of positive terms the difference between the fifth and fourth terms is 
, and the difference between the second and first terms is 
. What is the sum of the first five terms of this series?
Solution
Let the first term be 
and the common ratio be 
. Therefore, the second term is 
, the fourth term is 
, and the fifth term is 
. We're given that 
and 
. Dividing this first equation by this second one, we get 
. Therefore, 
, so 
.
Therefore, the first five terms of this series are 
, and their sum is 
.
See Also
| 1974 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 20 |
Followed by Problem 22 | |
| 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 | ||
| All AHSME Problems and Solutions | ||
