The document discusses arithmetic sequences and how to find missing or future terms in an arithmetic sequence using the formula an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the number number, and d is the common difference. It provides examples of arithmetic sequences and asks the reader to identify whether example sequences are arithmetic or not. It also gives illustrative examples of using the formula to find specific terms in arithmetic sequences.

1. Geometric
Sequence

2. Activity 1:
NEXT PICTURE PLEASE!!!
Examine the picture below and answer the
given question.

3. Can you solve the sequence?

4. 4

5. Which number is missing?
3

6. 30

7. 40

8. Arithmetic Sequence
An arithmetic sequence is a sequence where each
succeeding term is obtained by adding a fixed
number. The fixed number is called the common
difference which is denoted as d. To find the next
terms in an arithmetic sequence, we use the
formula:
an = a1 + (n – 1)d
where;
an – the last nth term
a1 – the first term
n – the number of terms in the sequence
D – common difference

9. Study the given examples below
and then identify if it is
arithmetic or not.
1. 10, 13, 16, 19,…
2. 2, 6, 18, 54…
3. 57, 49, 41
arithmetic
arithmetic
Not arithmetic

10. Illustrative Example 1
Determine the 10th term in the sequence
4, 6, 8, 10, ...
Illustrative Example 2
Find the 25th term of the arithmetic
sequence 3, 7, 11, 15, 19….
Illustrative Example 3
Find the 14th term of the sequence
23, 18,13, 8, 3…

11. Arithmetic means
The terms between any two nonconsecutive
terms of an arithmetic sequence
Examples:
1. Find two arithmetic means between 2 and 8.
2. Find three arithmetic means between 6 and 54
3. Find four arithmetic means between 68 and 3