Chapter 7: Q. 10 (page 591)

The Lucas numbers are defined recursively as follows:
$L_{1} = 1, L_{2} = 3,$ and $L_{k} = L_{k - 2} + L_{k - 1}$ for $k \geq 3$ .
What are $L_{3}, L_{4}, L_{5},$ and $L_{6}$ ?

Short Answer

Expert verified

The required values are $L_{3} = 4, L_{4} = 7, L_{5} = 11, L_{6} = 18$ .

Step by step solution

Step 1. Given information

$L_{1} = 1, L_{2} = 3$ .

L_{k} = L_{k - 2} + L_{k - 1}

where

k \geq 3

Step 2. Substitute k=3 and L1=1,L2=3 in the given sequence.

$L_{3} = L_{3 - 2} + L_{3 - 1} = L_{1} + L_{2} = 1 + 3 = 4$

Substitute $k = 4$ and $L_{2} = 3, L_{3} = 4$ in the given sequence.

$L_{4} = L_{4 - 2} + L_{4 - 1} = L_{2} + L_{3} = 3 + 4 = 7$

Step 3. Substitute k=5 and L3=4,L4=7 in the given sequence.

$L_{5} = L_{5 - 2} + L_{5 - 1} = L_{3} + L_{4} = 4 + 7 = 11$

Substitute $k = 6$ and $L_{4} = 7, L_{5} = 11$ in the given sequence.

$L_{6} = L_{6 - 2} + L_{6 - 1} = L_{4} + L_{5} = 7 + 11 = 18$

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The Lucas numbers are defined recursively as follows:
$L_{1} = 1, L_{2} = 3,$ and $L_{k} = L_{k - 2} + L_{k - 1}$ for $k \geq 3$ .
What are $L_{3}, L_{4}, L_{5},$ and $L_{6}$ ?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substitute k=3 and L1=1,L2=3 in the given sequence.

Step 3. Substitute k=5 and L3=4,L4=7 in the given sequence.

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The Lucas numbers are defined recursively as follows:L1=1,L2=3,and Lk=Lk-2+Lk-1for k≥3.What areL3,L4,L5,andL6?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substitute k=3 and L1=1,L2=3 in the given sequence.

Step 3. Substitute k=5 and L3=4,L4=7 in the given sequence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Decision Maths

Statistics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

The Lucas numbers are defined recursively as follows:
$L_{1} = 1, L_{2} = 3,$ and $L_{k} = L_{k - 2} + L_{k - 1}$ for $k \geq 3$ .
What are $L_{3}, L_{4}, L_{5},$ and $L_{6}$ ?