We have to match the sequence with the formulas.
The options for the sequences are:
• 3, 15, 75, 375
,• 18, 6, 2, 2/3
,• 17, 13, 9, 5
,• 1, 2, 4, 7
The first formula is:
[tex]a(n)=\frac{1}{3}\cdot a(n-1)[/tex]This is a geometric sequence, where the common ratio is 1/3.
This means that each term is reduced to 1/3 of the previous one.
This is the case for: 18, 6, 2, 2/3.
The second sequence is:
[tex]b(n)=b(n-1)-4[/tex]This is an arithmetic sequence with a common difference d = -4.
Each term is reduced by 4 units.
This corresponds to 17, 13, 9, 5.
The third sequence is:
[tex]c(n)=5\cdot c(n-1)[/tex]This is a geometric sequence with a common ratio r = 5.
This correspond to 3, 15, 75, 375.
The fourth sequence is:
[tex]d(n)=d(n-1)+n-1[/tex]This sequence increases by one less than the sequence step.
This matches with the sequence 1, 2, 4, 7.
Answer:
1) 18, 6, 2, 2/3
2) 17, 13, 9, 5
3) 3, 15, 75, 375
4) 1, 2, 4, 7