Pattern Detective! Part 2

What is the next number in this more sophisticated sequence? 1 , 4 , 5 , 9 , 14 , 23 , ? 1, 4, 5, 9, 14, 23, ?


The answer is 37.

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3 solutions

Munem Shahriar
Jun 14, 2017

Relevant wiki: Fibonacci Sequence

1 + 4 = 5

5 + 4 = 9

9 + 5 = 14

14 + 9 = 23

23 + 14 = 37

Next number is 37

Ashish Menon
May 31, 2016

In each case, the next number is the the number added to its predecessor. So, the answer is 14 + 23 = 37 14 + 23 = \color{#69047E}{\boxed{37}} .

Eric Hernandez
Aug 14, 2014

As you can see from the sequence, a n = a n 1 + a n 2 a_{n}=a_{n-1}+a_{n-2} and a 1 = 1 , a 2 = 4 a_{1}=1, a_{2}=4 . Therefore, the next term would be 14 + 23 = 37 14+23=\color{#69047E}{37} .

A closed form would be a n = 3 L n F n 2 a_{n}=\frac{3L_{n}-F_{n}}{2} , where L n L_{n} denotes the nth Lucas number and F n F_{n} denotes the nth Fibonacci number .

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