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The sequence $1,$ $1,$ $2,$ $3,$ $5,$ $8,$ $13,$ $21,$ $\dots$ 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 $4?$

 Jan 6, 2023
 #1
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This is the Fibonacci sequence and every 6th term is a multiple of 4.

 

Therefore: Floor[1000 / 6] = 166 such integers that are divisible by 4

 Jan 6, 2023
 #3
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The answer is actually 250, but thanks for the help.

Guest Jan 9, 2023

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