Identify the Sequence
Sequence: 3, 6, 9, 12 …
Is it arithmetic, geometric, or neither?
Arithmetic (adds 3 each time)
Write a recursive formula for the sequence 2, 5, 8, 11 …
f(1)=2, f(n)=f(n–1)+3, n≥2
What makes a sequence arithmetic?
Each term increases or decreases by a constant common difference.
If a sequence graph forms a straight line, what type is it?
Arithmetic
A sequence starts 3, 9, 27, … Find f(6).
729
Sequence: 2, 6, 18, 54 …
Is it arithmetic, geometric, or neither?
Geometric (multiply by 3 each time)
Write an explicit formula for the sequence 2, 5, 8, 11 …
f(n)=3n–1, n≥1
What makes a sequence geometric?
Each term is multiplied by a constant ratio (growth factor).
If a sequence graph curves exponentially upward, what type is it?
Geometric
Given an arithmetic sequence with f(1)=–2 and d=4, find f(10).
34
Sequence: 10, 7, 4, 1 …
What's the common difference?
-3
If f(1)=3 and f(n)=2·f(n–1), write the explicit form.
f(n)=3·2^(n–1) n≥1
Which Sequence is geometric?
A) 4, 8, 12, 16 B) 4, 8, 16, 32
B
Which sequence would match a decreasing line graph?
A) f(n)=2n+3 B) f(n)=–3n+10
B (negative slope)
For f(1)=5, f(2)=10, find the recursive and explicit forms if it’s geometric.
Recursive: f(n)=2·f(n–1) n≥2 f(1)=5
Explicit: f(n)=5·2^(n–1) n≥1
Sequence: 1, –2, 4, –8 …
Describe the pattern and classify the sequence.
Multiply by -2
Geometric
A sequence is defined by f(1)=–4, f(n)=f(n–1)+5. Find f(6).
f(6)=21
Given an arithmetic sequence f(1)=7 and f(5)=19, find the common difference.
3
A graph shows points (1, 81), (2, 27), (3, 9), (4, 3)… Describe the relationship. (arithmetic/geometric)
A paper has area 81 cm² and each cut reduces it to 1/3 of the previous. Find area after 5 cuts.
1/3 cm^2
The sequence f(1)=8, f(2)=4, f(3)=2, f(4)=1 …
Is it arithmetic or geometric and what is common difference or growth factor?
Geometric
Growth Factor:
1/2
Convert the explicit rule f(n)=5·(–2)^(n–1) to recursive form.
f(1)=5, f(n)=–2·f(n–1), n≥2
If a geometric sequence has f(1)=81 and f(3)=9, find the common ratio.
1/3
If the graph of a sequence approaches zero but never reaches it, what can you infer about the ratio?
The sequence is geometric with growth factor between 0 and 1.
Given f(1)=4, f(n)=f(n–1)+2n–1, find f(4).
f(4)=19