Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1)
Write the first four terms of the sequence an= n[9 +8(–1)n].
Answer:
1, 34, 3, 68
2)
Find the 67th term of the sequence defined by an=n + 3
n – 1.
Answer:
35
33
3)
Find the first five terms of the sequence defined by the recursive formula a1= 2, an=4an – 1 – 1 for n 2.
Answer:
2, 7, 27, 107, 427
4)
Find the general term of a sequence whose first four terms are 3
5, 6
6, 9
7, 12
8.
Answer:
3n
n + 4
5)
Write 4
k=1
k
k + 13 without summation notation. Do not evaluate.
Answer:
1
14 +2
15 +3
16 +4
17
6)
Write the following sum using summation notation: 1
2–2
3a +3
4a2–4
5a3 . . . +15
16a14
Answer:
15
k=1(–1)n + 1 n
n + 1an – 1
7)
Write the alternating series –1
2+1
3–1
4+1
5–1
6 using summation notation with the summing index k starting
at k = 1.
Answer:
5
k=1
(–1)k
k + 1
8)
Find the 300th term and the sum of the first 300 terms for the arithmetic sequence 8, 11, 14, . . .
Answer:
a300= 905, s300= 136,950
1
9)
Indicate by letter which of the following sequences can be the first three terms of an arithmetic sequence and state the
common difference for those that are.
(A) 9, 3, –3, . . . (B) 2, 6, 10, . . . (C) 5, 8, 12, . . .
Answer:
(A) Common difference = –6(B) Common difference = 4
10)
Find the sum of all the odd integers between 52 and 346.
Answer:
29,253
11)
Indicate by letter which of the following sequences can be the first three terms of a geometric sequence and state the
common ratio for those that are.
(A) 1, –4, 16, . . . (B) 14, 2, 2
7, . . . (C) 1, –8, –64, . . .
Answer:
(A) Common ratio = –4(B) Common ratio =1
7
12)
Find the sum of the first 25 terms of the geometric sequence 250, 250(1.05), 250(1.05)2, . . .
Answer:
11,931.77
13)
Find the common ratio of a geometric sequence if the first term is 5 and the 12th term is 30.
Answer:
1.18
14)
Find the sum of the infinite geometric sequence (if it exists): 7, 7
5, 7
25, . . .
Answer:
35
4= 8.75
15)
Find the sum of the infinite geometric sequence (if it exists): 4, –8
3, 16
9, –32
27, . . .
Answer:
12
5= 2.4
16)
If a person borrows $13,200 and agrees to repay the loan by paying $200 per month to reduce the loan and 1% of
the unpaid balance each month for using the money, what is the total cost of the loan over 66 months?
Answer:
$4,422
17)
Evaluate: 46!
38!8!
Answer:
260,932,815
18)
Evaluate: C40, 37
Answer:
9,880
19)
Expand: (3x + y)4
Answer:
81x4+108x3y +54x2y2+12xy3+y4
20)
Find the sixth term in the expansion of (p – 2q)12.
Answer:
–25,344p7q5
2