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14.1 Arithmetic Sequences
OBJ: • Find terms of
arithmetic sequences
Arithmetic progressions or sequences (A.P.) have a common difference d between each term.
To find d, take any term minus the term before it.
EX: For each progression that is an A.P., find the common difference d. Give a reason
for each answer. 3,3+25, 3+45,… Answer
3+25 – 3 =
25
A.P.
Reason
d = 25
3+25 + 25 =
3+45
EX: For each progression that is an A.P., find the common difference d. Give a reason
for each answer. -4.3,-2.8,-1.3, .2,… Answer
.2 – -1.3 =
1.5
A.P.
Reason
d = 1.5
-4.3 + 1.5 =
-2.8
EX: For each progression that is an A.P., find the common difference d. Give a reason
for each answer. 6.2, 4.4, 2.6, 0.8,… Answer
4.4 – 6.2 =
-1.8
A.P.
Reason
d = -1.8
4.4 + -1.8 =
2.6
EX: For each progression that is an A.P., find the common difference d. Give a reason
for each answer. 5, 10, 20, 40, . . . Answer
Not A.P.
Reason
10 – 5 ≠
20 – 10
Write the next three terms of the A.P.: 1, 1, 7, 5, . . .
8 2 8 4 4 – 1
8 8
3
8
10
8
13
8
16
8
(or 2)
19
8
Write the first four terms of the A.P. whose first term a is 7.5 and
common difference d = -3.7.5 – 3
4.5 – 3
1.5 – 3
-1.5
The nth term of an arithmetic progression or sequence is given by the formula: l = a + (n – 1) dFind the 36th term of
14, 10, 6, 2,…
10 – 14 =
-4
14 + 35(-4)
14 – 140
-126
Find the 26th term of
8, 5.4, 2.8, 0.2,…
5.4 – 8 =
-2.6
8 + 25(-2.6) =
8 – 65 =
-57
The nth term of an arithmetic progression or sequence is given by the
formula: l = a + (n – 1) dFind the 31st term of 3-2,1,-1+2,...
-1+2 – 1 =
-2+2 =
3-2 + 30(-2 + 2) =
3-2 – 60 + 302) =
-57 + 292
14.4 Geometric Sequences
OBJ: • Find terms of
geometric sequences
Geometric progressions or sequences (G.P.) have a common ratio r between each term
To find r, take any term divided by the
term before it.
EX: For each progression that is an G.P., find the common ratio r. Give a reason for
each answer. 5, 52, 10, 102,...Answer
52
5
2
G.P.
Reason
r = 2
52 • 2 =
10
EX: For each progression that is an G.P., find the common ratio r. Give a reason for
each answer. -8, 4, -2, 1,…Answer
4
-8
-1
2
Reason
r = -1
2
• -1
2 =
-2
EX: For each progression that is an G.P., find the common ratio r. Give a reason for
each answer. -2, -6, -18, -54,…Answer
-6
-2 =
3
Reason
r = 3-6 • 3
-18
EX: For each progression that is an G.P., find the common ratio r. Give a reason for
each answer. 2, 4, 6, 8, . . .Answer
8 ≠ 6 6 4
Not G.P.
Reason
Is an A.P. (d = 2)
EX: For each progression that is an G.P., find the common ratio r. Give a reason for
each answer. 3, .6, .12, .024, . . .Answer
.6
3 =
.2
Reason
r = .2
.6 • .2 =
.12
Write the next three terms of theG.P.: -1, 1, -1, 1, . . .
27 9 3 1
9_
-1
27
1 • -27
9
-3
1 • -3
-3 • -3
9 • -3
-27
Write the first four terms of the G.P. whose first term a is 0.04 and common ratio r = -10.
.04 • -10
-.4 • -10
4 • -10
-40
The nth term of an geometric progression or sequence is given by the formula: l = a •rn – 1
EX: 7th term:
a = 1 and r = -2
8
1 (-2)6
8
1 (64)
8
8
Find the 10th term of
the G.P.:
1, -1, 2, -4, . . .
2
1 (-2)9
2
1 (-512)
2
-256
The nth term of an geometric progression or sequence is given by the formula: l = a •rn – 1
Find the 10th term of the G. P.:
64, -32, 16, -8, …
64 (-1/2)9
64 • -1_
512
-1_
8