The document discusses arithmetic sequences and the concept of arithmetic means, explaining how to find specific terms and insert additional means between given numbers. It includes various exercises to practice finding arithmetic means and identifies key terms like arithmetic extremes and means. The material emphasizes the characteristics of arithmetic sequences and encourages engagement through problem-solving.

1. Arithmetic Means
Solomon Hippocrates S. Flores
E. Rodriguez Vocational High School

2. Find the specified term for each
arithmetic sequence.
1) 5, 8, 11, … 10th term

3. 2) 25, 20, 15, … 8th term

4. 3) 1, 6, 11, 16, … 6th term

5. 4) 10, 6, 2, -1, … 17th term

6. 5) 99, 88, 77, 66, … 18th term

7. Consider the following sequences:
1) 12, 26, 40, …
2) 300, 375, 450, …
3) 36, 33, 30, …
Do younotice anything?

8. Observe that…
1) 12, 26, 40, … 2) 300, 375, 450, … 3) 36, 33, 30, …
In general, a1, a2 and a3 are three
consecutive terms of an arithmetic sequence,
then the average of the first and the third
terms is the middle term, We can say that a2 is
the arithmetic mean of a1 and a3.

9. The arithmetic means are the
terms included between any two
consecutive terms of an arithmetic
sequence. The first and the last
terms in an arithmetic sequence
are called arithmetic extremes
while the terms in between are the
arithmetic means.

10. 3. Insert five arithmetic means between -4 and 38.
4. Insert six arithmetic means between -20 and -76.
5. If there are 14 arithmetic means between 25 and
85, find the 7th arithmetic mean.
Consider the following:
1. Find the arithmetic mean of 15 and 71.
2. Find the arithmetic mean between -8 and 24.
We can also insert more thanone arithmetic mean between any two
consecutive terms in an arithmetic sequence.

11. Solve the following:
1. Insert four arithmetic means between 2 and 14.
2. Insert four arithmetic means between -2 and
38.
3. Find an arithmetic mean between 49 and 9.
4. What are the three arithmetic means between
6.2 and 11?
5. If there are 8 arithmetic means between 10 and
50, find the 6th arithmetic mean.

12. Values integration
In his book Good to Great: Why Some Companies Make
the Leap.. And Others Don’t, Jim Collins wrote,
“By definition,it is not possiblefor everyone to be
above the average.”
Do you believe on this or not? Why?

13. Complete the following statements:
1. When three terms form an arithmetic
sequence, the _____________ is called the
arithmetic mean between the two terms.
2. The terms included ___________any two
____________ terms of an arithmetic sequence
are called ______________.
3. The first term and the __________ in an
arithmetic sequence are called arithmetic
___________ while the _______________ are
the arithmetic means.

14. Insert the indicated number of arithmetic means
between the two given numbers.
1) three; 10 and -10 6) four; ½ and 1/32
2) two; -3/4 and 1/4 7) three; 10 and -10
3) five; 4 and 40 8) four; 3 and 18
4) six; 1 and -20 9) five; 0 and -12
5) six; -23 and -44 10) three; 10 and 58

15. On your Math Time p. 9
Answer Practice Exercises 1.4
A 1 – 5 (Boys and Girls)
B Odd Numbers (Boys)
Even Numbers (Girls)

16. THANK YOU!