2022 AMC 12B Problems/Problem 9
Problem
The sequence is a strictly increasing arithmetic sequence of positive integers such that What is the minimum possible value of ?
Solution 1
We can rewrite the given equation as . Hence, must be a power of and larger than . The first power of 2 that is larger than , namely , does satisfy the equation: . In fact, this is the only solution; is exponential whereas is linear, so their graphs will not intersect again.
Now, let the common difference in the sequence be . Hence, and . To minimize , we maxmimize . Since the sequence contains only positive integers, and hence . When , .
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See also
2022 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
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