Redwood High School. Department of Mathematics
Name:___________________________________
2016-2017 Honors Advanced Algebra Test S1 #1 Prep wkst v1.0 .
Identify the sequence as arithmetic, geometric, or neither.
1) 4, 16, 64, 256, 1024, . . .
1)
2)
1 1 1 1
,
,
,
,...
10 15 20 25
3) 2,
n=0
2)
7
13
, 5,
,...
2
2
3)
6)
7) 2 5 + 3 5 + 4 5 + . . . + 7 5
7)
5
10) a n = n 2 - n, 1
n
11) a n = 2n - 1 , 1
n
12) 2 - 1 +
1 1 1
- +
2 4 8
Find the sum of the series.
4
(-1)k(5)k
13)
k=1
5
16)
17) a 1 = -2, a n = a n-1 + 4
17)
18) a 1 = -1, a n = 2an-1
18)
20)
Find the first five terms of the infinite sequence whose
nth term is given.
(-1)n + 1 n
x
21) a n =
21)
n+1
9)
5
16) a 1 = -1, a n = 3 - a n-1
20) The eighteenth term of
the arithmetic sequence 0,
13, 26, . . .
Find all the terms of the finite sequence.
1
,1 n 5
8) a n =
8)
n2
9) a n = 3 n , 1 n
14)
Find the indicated term of the sequence.
19) The thirteenth term of the
19)
arithmetic sequence 25,
22, 19, . . .
Express the sum using summation notation.
5) 3 + 6 + 9 + . . . + 18
5)
1 2 1 ... 4
+ + +
+
4 5 2
5
2
7n
Find the first six terms of the sequence.
1
15) a 1 = 9, a n = 1 15)
an - 1
Find the nth term and the indicated term of the arithmetic
sequence whose initial term a and common difference d
are given.
4) a = 4, d = -10
4)
a n = ? a 15 = ?
6)
(-1)n
14)
22) a n = (-1)n - 1
10)
n+3
2n - 1
23) a n = n 2 - n
22)
23)
11)
Find the first term and the common ratio for the geometric
sequence. Round approximations to the nearest
hundredth.
12)
13)
1
24) a 2 = -9.6, a8 = -161.06
24)
25) a 2 = 56, a5 = 7
25)
Solve the problem.
26) A brick staircase has a
total of 20 steps The
bottom step requires 108
bricks. Each successive
step requires 4 less bricks
than the prior one. How
many bricks are required
to build the staircase?
28) Find the sum of the first
225 positive even
integers.
28)
29) Suppose you just received
a job offer with a starting
salary of $37,000 per year
and a guaranteed raise of
$1500 per year. How
many years will it be
before you've made a
total (or aggregate) salary
of $1,025,000?
29)
26
32)
i=1
33) 7 +
9 i-1
8
7
7
7
+
+
+...
5 25 125
20 -
34)
i=1
1 i-1
5
39
i=1
27)
20 80 320
+...
31) -5 3
9
27
i=1
36)
27) A local civic theater has
22 seats in the first row
and 21 rows in all. Each
successive row contains 3
additional seats. How
many seats are in the civic
theater?
Evaluate the series, if it converges.
18 36 72
+...
30) -9 5 25 125
32 -
35)
26)
37)
k=1
38) 12 -
2 i-1
3
9 i-1
8
7 k
10
12 12 12
+
+...
5
25 125
35)
36)
37)
38)
Find the sum of the given infinite geometric series if
possible. Write the answer as a decimal number if
appropriate.
5
5
+...
39) 20 + 5 + +
39)
4 16
40)
2-
1 i
4
40)
2-
1 i
4
41)
i=1
41)
i=1
Write the series in summation notation. Use the index i
and let i begin at 1 in each summation.
1 1
1
1
+
-...
42) 1 - + 42)
4 9 16 25
30)
43) 6 + 18 + 30 + 42 + 54
43)
44) -3 + 4 - 5 + 6 - 7 + 8
44)
31)
Find the required part of the geometric sequence.
45) Find the common ratio for 45)
a geometric sequence
with the first term 4 and
fifth term 64.
32)
33)
46) Find the number of terms
of a geometric sequence
with the first term 3,
common ratio -3, and last
term 243.
34)
2
46)
47) Find the first term of a
geometric sequence with
the sixth term
and
common ratio of -3.
48) Find the first term of a
geometric sequence with
the sixth term 19,683 and
common ratio of -3.
4
49)
k(k + 3)
47)
n=7
60) 15 + 3 +
48)
5 5 5
, , , ...
2 4 8
5
7n
n=0
62) 4 + 8 + 16 + 32 + 64
62)
64)
5
i=1
1 i
(4)
3
Evaluate the sum.
4
(k2 - 2)
56)
2
k=1
57)
4000
i
51)
2500
2
52)
66)
53)
5
i=1
63)
64)
4 k
(2)
3
67) -4 - 5 -
25 125
+...
4
16
65)
66)
67)
Write a formula for the nth term of the arithmetic
sequence. Do not use a recursion formula.
68) 0.13, 0.16, 0.19, 0.22, 0.25, . 68)
..
55)
69)
5
k=2
56)
57)
1 i
5
j
65) 0.7 + 0.07 + 0.007 + . . .
i=1
58)
9 27
81
+...
5 25 125
j=200
Find the sum of the geometric series.
5
4(-3)i
54)
54)
i=1
55)
60)
61)
k=1
53)
3
3
+
+...
5 25
61) a 2 = -18, a4 = -162
63) -3 -
Write a formula for the nth term of the given geometric
sequence. Do not use a recursion formula.
1
1
1
1
,,, ...
50) - , 50)
5
20
80
320
52) 5,
59)
49)
k=2
51) 2, 4, 8, 16, 32, ...
1
5n
59)
58)
3
(-1)k + 1(k + 4)2
69)
Answer Key
Testname: HADVALG S1 TEST 1 SEQUENCES PREP V1.0
1)
2)
3)
4)
Geometric
Neither
Arithmetic
a n = 14 - 10n, a 15 = -136
6
3k
5)
k=1
12
k
6)
k+ 3
k=1
7
k5
7)
k=2
1 1 1 1
,
8) 1, , ,
4 9 16 25
9) 3, 9, 27, 81, 243
10) 0, 2, 6, 12, 20
11) 1, 3, 5, 7, 9
5
1 i-1
212)
2
i=1
13) 10
7
14)
4
15) 9,
8
1
8
1
, - , 9, , 9
8
9
8
16) -1, 4, -1, 4, -1, 4
17) -2, 2, 6, 10, 14, 18
18) -1, -2, -4, -8, -16, -32
19) -11
20) 221
1
1
1
1
1
21) x, - x2 , x3 , - x4 , x5
2
3
4
5
6
22) 4, -
5 6
8
, , - 1,
3 5
9
23) 0, 2, 6, 12, 20
24) a 1 = 6, r = -1.6
25) a 1 = 112, r = 0.5
26) 1400 bricks
27) 1092 seats
28) 50,850
29) 20 years
30) - 15
31) Does not converge
32) Does not converge.
35
33)
4
4
Answer Key
Testname: HADVALG S1 TEST 1 SEQUENCES PREP V1.0
34)
50
3
35)
96
5
36) Does not converge.
7
37)
3
38) 10
39) 26.67
40) -0.4
41) -0.4
42)
43)
44)
i=1
5
i=1
6
(-1)i+1
i2
(12i - 6)
(-1)i · ( i + 2 )
i=1
45) 2
46) 5
4
47) 3
48) - 81
49) 56
50) a n = -
1 1 n-1
5 4
51) a n = 2 n
52) a n = 5
53)
1 n-1
2
35
6
54) -732
1364
55)
3
56) 11
57) 8,002,000
58) 0.5
1
59)
62,500
60) 18.75
61) a 1 = 6, r = -3
62)
6
2i
i=2
5
Answer Key
Testname: HADVALG S1 TEST 1 SEQUENCES PREP V1.0
63) -
15
2
64) 3,106,350
65)
0.7(0.1)i-1
i=1
248
66)
3
67) Does not converge
68) a n = 0.03n + 0.1
69)
6