Presented by: Joseph C. Nilo

Practice Exercise:

Find the next five terms of the following sequence:

• 1, 3, 5, 7, …

• 2, 4, 6, 8, …

• 1, 5, 9, 8, …

• -7, -2, 3, 8, …

• 20, 11, 2, -7, …

Problem of the day!!!

• Find the common difference and the requires term in the following sequence

• 3, 6, 9, … a8

• -5, -10, -15, … a20

• 8, -1, -10, -19, … a18

Arithmetic Sequence

• A sequence in which each term is obtained by adding a constant d to preceding term. The constant number d is called the common difference.

• The nth term of an arithmetic sequence is defined as

an = a1 + (n – 1)d

an = a1 + (n – 1)d

where – an = the last term

– a1 = the first term

– n = the number of term– d = the common

difference

• State whether or not each of the following is an arithmetic progression. If it is, give the common difference. 5, 10, 15, … -5, 6, 10, … 4, 5, 6, 7, … 6, 20, 30, … ½, ¼, 1/6, …

d = 5not

not

d = 1

not

• Find the indicated term of the arithmetic sequence.

1. a1 = 10, d = 6, find a7

2. a1 = 12, d = 2, find a10

3. a1 = -5, d = -7, a12 = ?

4. a1 = -20, d = -4, a8 = ?

5. a1 = 0.5, d = 1.5, find a28

46

30

-82

-48

41

• Find the indicated term of the arithmetic sequence.

1. 12, 20, 28, … find a25

2. -5, -13, -21, … find a43

3. 2.5, 7, 11.5, … find a9

4. 15, 17, 19, … find a35

5. -3.8, -6.2, -8.6, … find a20