Fibonacci multiples

how many terms among the first 999992 terms of the FIBONACCI SEQUENCE are divisible by 7 ?


The answer is 124999.

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2 solutions

Vaibhav Prasad
Feb 17, 2015

The Fibonacci sequence goes as follows

1 1 2 3 5 8 13 21 21 34 55 89 144 233 377 610 987 987 1597...........

We observe that every 8 t h 8th term in the series is divisible by 7.

Thus 999992 8 \frac { 999992 }{ 8 } gives us 124999 124999

Nice observation!!@Vaib

Harsh Shrivastava - 6 years, 3 months ago

Well, your conjecture is correct, but how do you prove that this pattern follows for all Fibonacci numbers?

Anupam Nayak - 5 years, 4 months ago
Ayon Ghosh
Feb 22, 2017

Observe that every 8 t h 8th term in the Fibonacci Sequence is a multiple of 7 7 .Hence 999992 999992 terms will have 999992 / 8 999992/8 multiples i.e. 124999 124999 multiples of 7 7 .

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