Unit 6 Arithmetic and Geometric Sequences Quiz Review

IB Math Studies Yr 1

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6-5 Quiz Review

Unit 6 Arithmetic and Geometric Sequences Quiz Review

Directions: Complete each question to the best of your ability. You may use your notes. Be sure to clearly mark your

answers and work. Unless otherwise stated leave all answers as exact or rounded to 3 significant figures.

To receive full credit, you must complete the following: Show all of your work Check your work using the answer key. Show evidence of checking your work

(correct any mistakes IN A DIFFERENT COLOR)

DEFINITION

ARITHMETIC SEQUENCE

add to get next term (common difference)

GEOMETRIC SEQUENCE

multiply to get next term (common ratio)

KEY WORDS

"arithmetic", "common difference"

"geometric", "common ratio"

FORMULA (rule)

= 1 + ( - 1) = 2 - 1

= 1 -1

FINDING THE PATTERN

or

=

2 2

- -

1 1

=

2 1

1. Only one of the following four sequences is arithmetic and only one of them is geometric.

an = 1, 2, 3, 5, ...

bn

=

1,

3 2

,

9 4

,

27,

8

...

cn

=

1,

1 2

,

1 3

,

14,

...

dn = 1, 0.95, 0.90, 0.85, ...

State, with a reason, which sequence is

(a) arithmetic;

(b) geometric.

IB Math Studies Yr 1 2. Consider the sequence 2, 9, 16, 23, 30, ...

(a) Find the common difference. (b) What is the nth term of the sequence? (c) Find the 100th term of the sequence.

3. Consider the geometric sequence 24, a, 6, b, ... for which the common ratio is - 12. (a) Find the values of a and b. (b) What is the nth term of the sequence? (c) Find the exact value, in fraction form, of the eighth term.

IB Math Studies Yr 1 4. The sixth term of an arithmetic sequence is 24. The common difference is 8. (a) Calculate the seventh term of the sequence. (b) Write the nth term of the sequence. (c) Which term of the sequence is 336.

5. A geometric sequence has all its terms positive. The third term is 4 and the fifth term is 16. (a) Find the common ratio. (b) Which term of the sequence is 2048.

IB Math Studies Yr 1 6. The third term, 3, of a geometric sequence is 125. The fourth term, 4, is 100. (a) Find the common ratio of the sequence. (b) Find 1, the first term of the sequence. (c) Write the nth term of the sequence.

7. The fifth term, 5, of an arithmetic sequence is 2.25. The twenty-first term, 21, is 6.25. (a) Find the common difference of the sequence. (b) Find 20, the twentieth term of the sequence.

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