Middle School Madness

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Lucas Sequence

Posted: February 17, 2025

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A Lucas Sequence is similar to the famous Fibonacci Sequence.  For a Lucas sequence, you can begin with any two numbers (not 1, 1) and then continue with the next number determined by the sum of the two preceding numbers.  If the first two numbers are 2 and 7, the third number in the Lucas sequence is 2 + 7 = 9 to form 2, 7, 9 and the fourth number determined by 7 + 9 = 16.  The fifth number is determined by 9 + 16 = 25.  This produces the following sequence of numbers:  2, 7, 9, 16, 25, 41, 66, 107, 173, . . . 

Find the 31st number in this Lucas Sequence. 

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