2 A Fibonaccitype sequence that has been studied by mathemat

2.

A? Fibonacci-type sequence that has been studied by mathematicians is the Lucas? sequence, named after a French mathematician of the nineteenth century. The first ten terms of the Lucas sequence are? 1, 3,? 4, 7,? 11, 18,? 29, 47,? 76, 123. What is the eleventh term of the Lucas? sequence?

The eleventh term of the Lucas sequence is

This Question: 1 pt 7 of 10 (0 complete This Quiz: 10 pts possible The following pattern is established involving terms the Fibonacci sequence. Use inductive reasoning to make a conjecture concerning the next equation in the pattern and verify it. You may wish to refer to the first few terms or the sequence given in the text. 1-1 1 +2 3 1 2 5-8 +2 +5+ 133 2 2 +5 13 34 55 Each equation skips the next Fibonacci number to add the one afte Each side or the net equation will equal Following the patte write the next equation. The next equation in the listis written as (Do not evaluate. Use integers for any numbers in the expression

Solution

lucas sequence is a sequence in which a term is the sum of the last two term

1+3=4

3+4=7

4+7=11

7+11=18

11+18=29

18+29=47

29+47=76

47+76=123

76+123=199