Sequences Review

Find the Term

100

Given the arithmetic sequence 7, 10, 13, 16, ... what is the 5th term?

19

200

Given the geometric sequence 3, 6, 12, 24, ... what is the 6th term?

96

300

 In the sequence defined by the explicit formula f(n)=4n−1 , what is f(8)?

31

400

For the geometric sequence with first term 5 and common ratio ½, find the 7th term.

.078125

500

A sequence starts 2, 5, 14, 41, ... and follows the rule f(n)=3f(n-1)-1. What is the 6th term?

365

What's the Pattern

100

Determine whether the sequence 2, 4, 6, 8, ... is arithmetic, geometric, both, or neither. Give the rule.

Arithmetic

Adding 2 each time.

200

 Identify the pattern type and the common ratio or difference for 16, 8, 4, 2, ..

Geometric

Multiply by 1/2 each time (or divide by 2 each time)

300

Determine if the data below represents a geometric sequence. If so, give the ratio.

81, 27, 9, 3

yes

1/3

400

Determine whether the sequence 1, 2, 4, 7, 11, 16, ... follows an arithmetic, geometric, or neither. Describe the pattern and predict the next two terms.

Neither

22, 29

500

The population of a town is recorded: 10,000; 9,500; 9,025; 8,573.75; ... Is this exponential growth, exponential decay, arithmetic, or neither? If exponential, state the growth/decay factor.

Exponential Decay

0.95

Recursive Formulas

100

Write a recursive formula for the arithmetic sequence 5, 8, 11, 14, ...

f(1)=5

f(n)=f(n-1)+3

200

 Give a recursive formula for the geometric sequence 6, 18, 54, ...

f(1)=6

f(n)=f(n-1)*3

300

Given the recursive formula for the sequence defined by:

f(1)=4 and f(n)=f(n-1)+3

Compute f(5) using the recursion.

16

400

A sequence has first term 7 and each term is 0.6 times the previous term. Write the recursive formula and find f(6).

f(1)=7

f(n)=f(n-1)*0.6

f(6)=.55432

500

 For the sequence defined by a₁=2 and a_n+1=5a_n+1, use the recursive formula to calculate a₄.

281

Classify the Sequence

100

Classify 10, 20, 30, 40, ... as arithmetic, geometric, both, or neither. State the common difference or ratio.

Arithmetic

Common Difference = 10

200

Classify 9, 3, 1, 1/3, ... and give the common ratio if geometric.

Geometric

Common Ratio = 1/3

300

The sequence 2, 4, 8, 16, ... is which type?

Geometric

400

Given the sequence -5, -2, 1, 4, 7, ... classify it and find the common difference.

Arithmetic

3

500

A sequence is 100, 90, 81, 72.9, ... Classify it and explain whether it represents exponential decay. If so, provide the decay factor.

Geometric

0.9

Explicit Formulas

100

Write the explicit (nth-term) formula for the arithmetic sequence 2, 5, 8, 11, ... .

f(n)=2+3(n-1)

200

Write the explicit formula for the geometric sequence 4, 12, 36, 108, ..

f(n)=4*3^n-1

300

Given the recursive arithmetic rule a₁=3 and 

a_n=a_n-1+7, write the explicit formula and find a₁₀.

f(n)=3+7(n-1)

f(10)=66

400

Write the explicit formula for the geometric sequence with a₁=5 and common ratio r=−2. Then find a₆.

f(n)=5*(-2)^n-1

-160

500

Given the recursive formula:

f(1)=3

f(n)=f(n-1)*5

Write the explicit formula

f(n)=3*5^n-1