21. The Fibonacci sequence is formed by adding the previous two numbers to get the next:
1, 1, 2, 3, 5, 8, 13 ,...
What are the next three numbers in this sequence?
The Lucas Sequence has the same rule but starts with 1 and 3.
(i) Write out the first 7 terms of the Lucas sequence.
(ii) Write down the first 7 terms, in terms off and J, for the sequence with the same rule whose first terms are x and y.
(iii) Mia says: “If x is a multiple of 5 then the 6th term of the sequence is also a multiple of 5 whatever y is”.
Do you agree? Explain your reasoning carefully.