1. OBJ: • Find terms of arithmetic sequences

2. Arithmetic progressions or sequences (A. P
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.

3. EX:  For each progression that is an A. P
EX:  For each progression that is an A.P., find the common difference d. Give a reason for each answer. 3,3+25, 3+45,…
Answer
3+25 – 3 =
25
A.P.
Reason
d = 25
3+25 + 25 =
3+45

4. EX:  For each progression that is an A. P
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
 =
-2.8

5. EX:  For each progression that is an A. P
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
 =
2.6

6. EX:  For each progression that is an A. P
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

7. Write the next three terms of the A.P.: 1, 1, 7, 5, . . . 8 2 8 4
4 – 1 8 3
(or 2) 19

8. Write the first four terms of the A. P. whose first term a is 7
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

9. The nth term of an arithmetic progression or sequence is given by the formula: l = a + (n – 1) d
Find the 36th term of
14, 10, 6, 2,…
10 – 14 = -4
(-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

10. The nth term of an arithmetic progression or sequence is given by the formula: l = a + (n – 1) d
Find the 31st term of 3-2,1,-1+2,...
-1+2 – 1 =
-2+2 =
3-2 + 30(-2 + 2) =
3-2 – 2) = 2

11. OBJ: • Find terms of geometric sequences

12. Geometric progressions or sequences (G. P
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.

13. EX:  For each progression that is an G. P. , find the common ratio r
EX:  For each progression that is an G.P., find the common ratio r. Give a reason for each answer. 5, 52, 10, 102,...
Answer
52 5 2
G.P.
Reason
r = 2
 52 • 2 = 10

14. EX:  For each progression that is an G. P. , find the common ratio r
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
 4 • -1
2 = -2

15. EX:  For each progression that is an G. P. , find the common ratio r
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

16. EX:  For each progression that is an G. P. , find the common ratio r
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
Not G.P.
Reason
Is an A.P. (d = 2)

17. EX:  For each progression that is an G. P. , find the common ratio r
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

18. Write the next three terms of the G.P.: -1, 1, -1, 1, . . . 27 9 3
1 9_ •
1 • • -3 9 •

19. Write the first four terms of the G. P. whose first term a is 0
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

20. 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.:
1, -1, 2, -4, . . . 2
1 (-2)9
1 (-512)
-256
EX:  7th term:
a = 1 and r = -2 8
1 (-2)6
1 (64)

21. 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