Arithmetic and Geometric Sequences
Multiple Choice
Identify the choice that best completes the statement or answers the question.
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1. If
then
?
a. 5
b. –1
c. –3
2. The sequence 2.5, 5, 7.5, 10,... is
a. arithmetic
b. neither a or b
3. The sequence 1, 3, 7, 15,... is
a. geometric
b. neither a or b
4. What is the next number in the sequence
?
a. 450
b. 360
c. 400
d. 24
c. geometric
c. arithmetic
d. 810
5. If
then
?
a. 0.01171875
b. 10
c. 0.0234375
d. 19683
6. The sequence 8, 4, 2, 0,... is
a. arithmetic
b. geometric
c. neither a or b
7. The sequence 8, 3, -2, -7,... is
a. geometric
b. neither a or b
c. arithmetic
8. What is the next number in the sequence
?
a. 27
b. 2560
c. 44
d. 26
9. The sequence 2, 10, 50, 250,... is
a. neither a or b
b. geometric
c. arithmetic
10. The sequence 3, -4, 5, -6,... is
a. neither a or b
b. geometric
c. arithmetic
Arithmetic and Geometric Sequences
Answer Section
MULTIPLE CHOICE
1. ANS: B
Just plug in 7 for n in the formula and follow order of operations. (Subtract 1 first, then multiply by –1 and
then add 5)
Or just enter the formula on the calculator as
in the Y= menu (after switching the mode
from func(tion) to seq(uence) ), and then go to the home screen and enter...
and press return.
PTS: 1
2. ANS: A
The differences between successive terms is always 2.5, so the sequence is arithmetic (common difference).
PTS: 1
3. ANS: B
The differences between successive terms are 2, 4, 8 so the sequence is not arithmetic (these values would
have to be the same).
There is no number that can be multiplied by each term to get the next term, so the sequence is not geometric.
PTS: 1
4. ANS: D
Each term is 3 times the previous term (check by dividing consecutive terms), so if we take 270 and multiply
it by 3, we get 810.
PTS: 1
5. ANS: C
Just plug in 9 for n in the formula and follow order of operations. (Subtract 1 first, then evaluate the power,
and then multiply by 6)
Or just enter the formula on the calculator as
in the Y= menu (after switching the mode
from func(tion) to seq(uence) ), and then go to the home scren and enter...
and press return.
PTS: 1
6. ANS: C
The differences between successive terms are -4,-2,-2 so the sequence is not arithmetic (these values would
have to be the same).
There is no number that can be multiplied by each term to get the next term, so the sequence is not geometric.
PTS: 1
7. ANS: C
The differences between successive terms is always -5, so the sequence is arithmetic (common difference).
PTS: 1
8. ANS: D
Each term is 4 more than the previous term (check by subtracting consecutive terms), so if we take 22 and add
4 to it, we get 26.
PTS: 1
9. ANS: B
Each term is the previous term multiplied by 5, so the sequence is geometric. (It has a common ratio)
PTS: 1
10. ANS: A
The differences between successive terms are -7, 9, -11 so the sequence is not arithmetic (these values would
have to be the same).
There is no number that can be multiplied by each term to get the next term, so the sequence is not geometric.
PTS: 1