Analysis A - Barrington 220



Precalculus A 12-02 Worksheet Name ______________________

Finite Sequences

Section 12.3 Date _________ Period _______

Show that each of the following sequences are geometric by solving for the common ratio (see first problem as an example). Then, write out the first four terms.

1) [pic] 2) [pic]

3) [pic] 4) [pic]

5) [pic] 6) [pic]

Determine whether the following sequences are arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.

7) [pic] 8) [pic] 9) [pic]

10) 1, 3, 6, 10, . . . 11) 1, 1, 2, 3, 5, 8, . . . 12) [pic]

For the following problems, find the fifth term and [pic], the [pic] term, of the geometric sequence whose initial term a and common ratio r are given.

13) [pic] 14) [pic] 15) [pic]

Find the indicated term of each of the following geometric sequences.

16) 7th term of [pic] 17) 8th term of 1, 3, 9, . . .

18) 10th term of -1, 2, -4, . . . 19) 8th term of 0.4, 0.04, 0.004, . . .

20) You are interviewing for a job and receive two offers:

A: $20,000 to start, with guaranteed annual increases of 6% for the first 5 years.

B: $22,000 to start, with guaranteed annual increases of 3% for the first 5 years.

Which offer is best if your goal is to be making as much as possible after 5 years?

Which is best if your goal is to make as much money as possible over the life of the contract (5 years)?

Precalculus A 12-02 Worksheet Answer Key

Finite Sequences

Section 12.3

Show that each of the following sequences are geometric by solving for the common ratio (see first problem as an example). Then, write out the first four terms.

1) [pic] 2) [pic]

3) [pic] 4) [pic]

5) [pic] 6) [pic]

Determine whether the following sequences are arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.

7) [pic] 8) [pic] 9) [pic]

10) 1, 3, 6, 10, . . . 11) 1, 1, 2, 3, 5, 8, . . . 12) [pic]

For the following problems, find the fifth term and [pic], the [pic] term, of the geometric sequence whose initial term a and common ratio r are given.

13) [pic] 14) [pic] 15) [pic]

Find the indicated term of each of the following geometric sequences.

16) 7th term of [pic] 17) 8th term of 1, 3, 9, . . .

18) 10th term of -1, 2, -4, . . . 19) 8th term of 0.4, 0.04, 0.004, . . .

20) You are interviewing for a job and receive two offers:

A: $20,000 to start, with guaranteed annual increases of 6% for the first 5 years.

B: $22,000 to start, with guaranteed annual increases of 3% for the first 5 years.

Which offer is best if your goal is to be making as much as possible after 5 years?

Which is best if your goal is to make as much money as possible over the life of the contract (5 years)?

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