Clues are everywhere

Alice is puzzled by this question:

2 , 2 , 3 , 4 , 6 , 9 , ? 2, 2, 3, 4, 6, 9, ?

What is the next number in the sequence?


The answer is 14.

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3 solutions

F ( n ) = F ( n 1 ) + F ( n 2 ) 1 F(n)=F(n-1)+F(n-2)-1 ,we need F ( 7 ) F(7) , so n = 7 n=7 :-

F ( 7 ) = F ( 6 ) + F ( 5 ) 1 = 9 + 6 1 = 14 F(7)=F(6)+F(5)-1=9+6-1=14

Edwin Gray
Nov 6, 2018

Each number is 1 less than the sum of the 2 previous numbers. Ed Gray

Mohammad Farhat
Aug 15, 2018

There are two similar ways to solve this (to my knowledge).

The first is that each term is 1+ than the numbers in the Fibonacci sequence.

Fibonacci sequence : 1, 1, 2, 3, 5, 8, 13

COPIED Sequence : 1+1, 1+1, 2+1, 3+1, 5+1, 8+1, 13+1

Given this the answer is 14.

The second one is: It functions like the Fibonacci sequence but if it starts with n, n then the next term is 2n-1

2+2-1=3

2+3-1=4

3+4-1=6

4+6-1=9

6+9-1=14

Given this the answer is 14.

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