Name: 
 

Arithmetic Sequences


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Graph the first five terms of the sequence.

mc001-1.jpg
a.
mc001-2.jpg
d.
mc001-5.jpg
b.
mc001-3.jpg
e.
mc001-6.jpg
c.
mc001-4.jpg
 

 2. 
Find the first five terms of the sequence, the common difference d and graph the first five terms of the sequence.

mc002-1.jpg
a.
mc002-2.jpg
d.
mc002-5.jpg
b.
mc002-3.jpg
e.
mc002-6.jpg
c.
mc002-4.jpg
 

 3. 
The first term of the arithmetic sequence a is 4 and common difference d is 6. Find the nth term and the 10th term.
a.
mc003-1.jpg
b.
mc003-2.jpg
c.
mc003-3.jpg
d.
mc003-4.jpg
e.
mc003-5.jpg
 

 4. 
Find the common difference d of the arithmetic sequence.

4, 6, 8, 10, ...
a.
6
b.
n
c.
4
d.
2
e.
2n
 

 5. 
Find the common difference d of the following arithmetic sequence.

5, 9, 13, 17, ...
a.
mc005-1.jpg
b.
3
c.
16
d.
4
e.
20
 

 6. 
Find the first five terms and determine if the sequence is arithmetic.

mc006-1.jpg
a.
mc006-2.jpg The sequence is arithmetic.
b.
mc006-3.jpg The sequence is not arithmetic.
c.
mc006-4.jpg The sequence is arithmetic.
d.
mc006-5.jpg The sequence is arithmetic.
e.
mc006-6.jpg The sequence is not arithmetic.
 

 7. 
If it is arithmetic, express the nth term of the sequence in the standard form mc007-1.jpg and find the common difference.

mc007-2.jpg
a.
mc007-3.jpg
b.
mc007-4.jpg
c.
Not an arithmetic sequence.
d.
mc007-5.jpg
e.
mc007-6.jpg
 

 8. 
Find the fifth term of the arithmetic sequence.

2, 10, 18, 26, ...
a.
34
b.
26
c.
5
d.
27
e.
44
 

 9. 
Find the 60th term of the arithmetic sequence.

26.2, 29.9, 33.6, 37.3, ...
a.
8121
b.
244.5
c.
248.2
d.
1572
e.
251.9
 

 10. 
Find the nth term of the arithmetic sequence.

2, 2 + s, 2 + 2s, 2 + 3s, ...
a.
mc010-1.jpg
b.
mc010-2.jpg
c.
mc010-3.jpg
d.
mc010-4.jpg
e.
mc010-5.jpg
 

 11. 
Find the 18th term of the arithmetic sequence.

–t, – t + 3, – t + 6, – t + 9 ...
a.
45 – t
b.
51 – t
c.
54 – t
d.
57 – (n – 1)t
e.
3 – nt
 

 12. 
The 10th term of an arithmetic sequence is mc012-1.jpg and the second term is mc012-2.jpg. Find the first term.
a.
–4
b.
1
c.
–2.25
d.
–1
e.
0.25
 

 13. 
The 12th term of an arithmetic sequence is 13 and the 5th term is 6. Find the 22th term.
a.
24
b.
21
c.
23
d.
43
e.
10
 

 14. 
The 70th term of an arithmetic sequence is 107, and the common difference is 3. Find the first three terms.
a.
–100, –94, –88
b.
–103, –97, –91
c.
–97, –94, –91
d.
–100, –97, –94
e.
–103, –100, –97
 

 15. 
The 20th term of an arithmetic sequence is 97, and the common difference is 5. Find a formula for the nth term.
a.
5 + 2(n – 1)
b.
20 + 5(n – 1)
c.
2 + 5(n – 1)
d.
5 + 2(n + 1)
e.
2 + 5(n)
 

 16. 
Which term of the arithmetic sequence 3, 8, 13,... is 73?
a.
15
b.
13
c.
17
d.
16
e.
14
 

 17. 
Find the partial sum Sn of the arithmetic sequence that satisfies the following conditions.

a = 3, d = 5, n = 20
a.
103
b.
2020
c.
1010
d.
98
e.
1060
 

 18. 
A partial sum of an arithmetic sequence is given. Find the sum.

3 + 7 + 11 + ... + 39
a.
210
b.
189
c.
420
d.
60
e.
230
 

 19. 
A partial sum of an arithmetic sequence is given. Find the sum.

mc019-1.jpg
a.
78
b.
42
c.
12
d.
60
e.
97.5
 

 20. 
A partial sum of an arithmetic sequence is given. Find the sum.

mc020-1.jpg
a.
33.75
b.
37.5
c.
81
d.
25
e.
40.5
 

 21. 
Find the product of the numbers.

mc021-1.jpg
a.
190
b.
mc021-2.jpg
c.
mc021-3.jpg
d.
380
e.
mc021-4.jpg
 

 22. 
The harmonic mean of two numbers is the reciprocal of the average of the reciprocals of the two numbers. Find the harmonic mean of 1 and 3.
a.
1.5
b.
4
c.
0.25
d.
2
e.
1.73
 

 23. 
Telephone poles are stored in a pile with 30 poles in the first layer, 29 in the second, and so on. If there are 12 layers, how many telephone poles does the pile contain?

mc023-1.jpg
a.
288 poles
b.
294 poles
c.
42 poles
d.
588 poles
e.
19 poles
 

 24. 
A man gets a job with a salary of $30,000 a year. He is promised a $1,500 raise each subsequent year. Find his total earnings for a 15 year period.
a.
$607,500
b.
$1,215,000
c.
$51,000
d.
$618,750
e.
$52,500
 

 25. 
An architect designs a theater with 25 seats in the first row, 29 in the second, 33 in the third, and so on. If the theater is to have a seating capacity of 4,120, how many rows must the architect use in his design?
a.
50
b.
42
c.
40
d.
45
e.
35
 

Numeric Response
 

 26. 
The 12th term of an arithmetic sequence is 34, and the fifth term is 20. Find the 20th term.

a20 = __________

 

 27. 
The first term of an arithmetic sequence is 3, and the common difference is 2. Is 5,981 a term of this sequence? If so, which term is it?

 

 28. 
Find the partial sum nr028-1.jpg of the arithmetic sequence that satisfies the given conditions.

nr028-2.jpg

Sn = __________

 

 29. 
Find the partial sum nr029-1.jpg of the arithmetic sequence that satisfies the given conditions.

nr029-2.jpg

Sn = __________

 

 30. 
A partial sum of an arithmetic sequence is given. Find the sum.

nr030-1.jpg

S = __________

 

 31. 
A partial sum of an arithmetic sequence is given. Find the sum.

nr031-1.jpg

S = __________

 

 32. 
An arithmetic sequence has first term nr032-1.jpg and fourth term nr032-2.jpg. How many terms of this sequence must be added to get 3,402?

n = __________

 

 33. 
An architect designs a theater with 28 seats in the first row, 32 in the second, 36 in the third, and so on. If the theater is to have a seating capacity of 1,020, how many rows must the architect use in his design?

__________ rows

 

Short Answer
 

 34. 
A sequence is given.

sa034-1.jpg

(a) Find the first five terms of the sequence.

a1 = __________

a2 = __________

a3 = __________

a4 = __________

a5 = __________

(b) What is the common difference d?

d = __________
 

 35. 
Find the nth term of the arithmetic sequence with given first term a and common difference d. What is the 10th term?

sa035-1.jpg

an = __________

a10 = __________
 

 36. 
Determine whether the sequence is arithmetic. If it is arithmetic, find the common difference.

5, 11, 13, 23, ...
 

 37. 
Determine the common difference, the fifth term, the nth term, and the 100th term of the arithmetic sequence.

3, 6, 9, 12, ...

d = __________

a5 = __________

an = __________ + __________ • (n – 1)

a100 = __________
 

 38. 
Determine the common difference, the fifth term, the nth term, and the 100th term of the arithmetic sequence.

–27, –18, –9, 0, ...

d = __________

a5 = __________

an = __________ + __________ • (n – 1)

a100 = __________
 

 39. 
Determine the common difference, the fifth term, the nth term, and the 100th term of the arithmetic sequence.

12, sa039-1.jpg, sa039-2.jpg, sa039-3.jpg, ...

d = __________

a5 = __________

an = __________ + __________ • (n – 1)

a100 = __________
 

 40. 
The 20th term of an arithmetic sequence is 116, and the common difference is 4. Find a formula for the nth term.

an = __________ + __________ • n
 

 41. 
The harmonic mean of two numbers is the reciprocal of the average of the reciprocals of the two numbers. Find the harmonic mean of 9 and 4.
 



 
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