2022 AMC 10B Problems/Problem 15
Contents
[hide]Problem
Let be the sum of the first terms of an arithmetic sequence that has a common difference of . The quotient does not depend on . What is ?
Solution 1
Let's say that our sequence is Then, since the value of n doesn't matter in the quotient , we can say that Simplifying, we get , from which Solving for , we get that .
Since the sum of the first odd numbers is , .
Solution 2 (Quick Insight)
Recall that the sum of the first odd numbers is .
Since , we have .
~numerophile
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See Also
2022 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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 | ||
All AMC 10 Problems and Solutions |
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