2022 AMC 10B Problems/Problem 6
Contents
[hide]Problem
How many of the first ten numbers of the sequence are prime numbers?
Solution 1 (Generalization)
The th term of this sequence is It follows that the terms are Therefore, there are prime numbers in this sequence.
~MRENTHUSIASM
Solution 2 (Educated Guesses)
Note that it's obvious that is divisible by and is divisible by therefore, since this an AMC 10 problem 6, we may safely assume that we do not need to check two-digit prime divisibility or use obscure theorems. So, the answer is
~Dhillonr25
Solution 3 (Simple Sums)
Observe how and and all take the form of which factors as Factoring each of the sums, we have and respectively. With each number factored, there are primes in the set.
~ab2024
See Also
2022 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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All AMC 10 Problems and Solutions |
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