The document discusses arithmetic sequences and how to find terms in arithmetic sequences. It defines an arithmetic sequence as a sequence where each term is obtained by adding a constant difference to the preceding term. It provides the formula for finding the nth term in an arithmetic sequence and works through examples of identifying arithmetic sequences and finding specified terms.

1. Presented by: Joseph C. Nilo

2. 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, …

3. 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

4. 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

5. a n = a 1 + (n – 1)d
where
– a n = the last term
– a 1 = the first term
– n = the number of term
– d = the common
difference

7. • 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 = 5
not
d = 1
not
not

8. • 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

10. • 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