Question

In a fibonacci sequence, the first number is 1 and the tenth number is 111. find the second number.

Answer 1

Let x be the second number in the Fibonacci sequence.

Then we have the sequence is as follows:

1st: 1
2nd: x
3rd: 1 + x
4th: 1 + 2x
5th: 2 + 3x
6th: 3 + 5x

7th: 5 + 8x

8th: 8 + 13x

9th: 13 + 21x

10th: 21 + 34x

so 111 = 21 + 34x, so 34x = 90, so x = 90/34 = 45/17.

Thus the second term would be 45/17. (if I haven’t made any errors in arithmetic).