he Lucas sequence is defined by L(1) = 1 L(2) = 3 L(n) =

Chapter 3, Problem 32

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QUESTION:

he Lucas sequence is defined by L(1) = 1 L(2) = 3 L(n) = L(n 1) + L(n 2) for n 2 a. Write the first five terms of the sequence. b. Prove that L(n) = F(n + 1) + F(n 1) for n 2 where F is the Fibonacci sequence.

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QUESTION:

he Lucas sequence is defined by L(1) = 1 L(2) = 3 L(n) = L(n 1) + L(n 2) for n 2 a. Write the first five terms of the sequence. b. Prove that L(n) = F(n + 1) + F(n 1) for n 2 where F is the Fibonacci sequence.

ANSWER:

Step 1 of 3

The given Lucas sequence is:

 for

The sequence is obtained by using this relation.

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