Describe how the sequences below are related.

(ii) 4, 4, 5, 6, 8, 11, 16, 24, . . .
(iii) -1, -1, 0, 1, 3, 6, 11, 19, . . .
(b) Describe how to find the next term of each sequence.

Hi, 

It is based on Fibonacci sequence. That states F(n)=F(n-1)+F(n-2)... so on. Where every term increased by 3, started with the term 1 and follows with 1, 1 (0+1), 2 (1+1), 3(1+2), 5 (2+3), 8 (3+5), 13 (5+8), 21 (8+13), 34 (13+21)... so on.

3 + 1 = 4

3 + 1 = 4

3 + 2 = 5

3 + 3 = 6

3 + 5 = 8

3 + 8 = 11

3 + 13 = 16

3 + 21 = 24

So, Next term of sequence is 37.

3 + 34 = 37


b)

Second series is similar but instead of +3 here -2 will be done 
1-2 = -1
1-2 = -1
2-2 = 0 
3-2 = 1 
5-2 = 3 
8-2 = 6 
13-2 = 11
21-2 = 19
so next term will next term of fibonacci series -2 
= 34-2 = 32
and so on

 

​Regards

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