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The sequence 1,1,2,3,5,8,13,21 has the property that each term (starting with the third term) is the sum of the previous two terms. How many of the first 1000 terms are divisible by 5?

 Aug 6, 2022
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This is the Fibonacci sequence and it begins like this:

 

{1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765}==20 terms

 

Every 5th term after the first 5 term is divisible by 5, or the 5th, 10th, 15th, 20th.....etc.

 

Therefore, the first 1,000 terms==1,000 / 5 ==200 terms that are divisible by 5

 Aug 6, 2022

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