Difference between revisions of "1981 AHSME Problems/Problem 14"
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Latest revision as of 14:02, 28 June 2025
Problem
In a geometric sequence of real numbers, the sum of the first terms is
, and the sum of the first
terms is
. The sum of the first
terms is
Solution 1
Denote the sum of the first terms as
. Since we know that the sum of the first
terms is
which is
, we have
+
+
=
because it is a geometric series. We can quickly see that
=
, and therefore, the sum of the first
terms is
~Arcticturn
See also
1981 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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 |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.