What is the next number in this more sophisticated sequence? 1 , 4 , 5 , 9 , 1 4 , 2 3 , ?
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In each case, the next number is the the number added to its predecessor. So, the answer is 1 4 + 2 3 = 3 7 .
As you can see from the sequence, a n = a n − 1 + a n − 2 and a 1 = 1 , a 2 = 4 . Therefore, the next term would be 1 4 + 2 3 = 3 7 .
A closed form would be a n = 2 3 L n − F n , where L n denotes the nth Lucas number and F n denotes the nth Fibonacci number .
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Relevant wiki: Fibonacci Sequence
1 + 4 = 5
5 + 4 = 9
9 + 5 = 14
14 + 9 = 23
23 + 14 = 37
Next number is 37