This document defines arithmetic mean and provides examples of calculating arithmetic means between given terms. It explains that the arithmetic mean is the term found between two extremes of an arithmetic sequence. It then gives 5 examples that demonstrate how to use the formula for an arithmetic sequence to calculate the arithmetic mean between two terms or insert additional terms. The examples calculate arithmetic means between various number ranges such as -12 and 4, 38 and 98, and -15 and 3. The last example finds the first 9 terms of a sequence when the 3rd term is 13 and the 9th term is 37.

1. ARITHMETIC
MEAN

2. 2TEACH A COURSE
ARITHMETIC MEAN
 The term of the arithmetic sequence that is between two given
terms
 Are term found between two extremes of an arithmetic sequence
denoted by m1, m2, m3, m4,…

3. FORMULA
3

4. 4TEACH A COURSE
EXAMPLE # 1: WHAT IS THE ARITHMETIC MEAN BETWEEN 85 AND 95
 85___95
 Use the formula of arithmetic sequence
 an=a1+(n-1)d

85__95
an=a1+(n-1)d
 a1=85 an=95 n=3 (3 terms) d=___?
 95 =85+(3-1)d
 95 =85+(2)d
 95-85=2d
 10=2d
 d=5
 85+5=90


5. 5TEACH A COURSE
EXAMPLE # 2: WHAT IS THE ARITHMETIC MEAN BETWEEN -12 AND 4?
 -12___4
 Use the formula of arithmetic sequence
 an=a1+(n-1)d
 a1=-12 an=4 n=3 (3 terms) d=___?
 4=-12+(3-1)d
 4=-12(2)d
 4+12=2d
 16=2d
 d=8
 -12+8=-4

6. 6TEACH A COURSE
EXAMPLE # 3: INSERT FOUR ARITHMETIC MEANS BETWEEN 38 AND
98.
 38___, ___, ____, ____98
 Use the formula of arithmetic sequence
 an=a1+(n-1)d
 a1=38 an=98 n=6 (6 terms)
d=___?
 98=38+(6-1)d
 98=38+(5)d
 98-38=5d
 60=5d
 d=12

7. 7TEACH A COURSE
EXAMPLE #4: INSERT 5 ARITHMETIC MEANS BETWEEN -15 AND 3.
 -15,___,___,___,___,___,3
 Use the formula of arithmetic sequence
 an=a1+(n-1)d
 a1=-15 an=3 n=7 (7 terms)
d=___?
 3=-15+(7-1)d
 3=-15+(6)d
 3+15=6d
 18=6d
 d=3

8. 8TEACH A COURSE
EXAMPLE #5: IF THE 3RD TERM OF THE ARITHMETIC SEQUENCE IS 13 AND
THE 9TH TERM IS 37. WHAT IS THE FIRST 9 TERMS OF THE SEQUENCE?
 ___,___,13___,___,___,___,___,37
 Use the formula of arithmetic sequence
 an=a1+(n-1)d
 a1=13 an=37 n=7 (7 terms)
d=___?
 37=13+(7-1)d
 37-13+(6)d
 24=6d
 d=4

9. 9TEACH A COURSE
ACTIVITY#2

10. 10TEACH A COURSE
1. IF THE 4TH TERM OF THE ARITHMETIC SEQUENCE IS 12, AND THE 12TH
TERM IS 56. FIND THE FIRST 7 TERMS OF THE ARITHMETIC SEQUENCE.

11. 11TEACH A COURSE
2. FIND 5 ARITHMETIC SEQUENCE BETWEEN 5 AND 10

12. 12TEACH A COURSE
3. INSERT 5 ARITHMETIC MEAN BETWEEN 5 AND 25

13. 13TEACH A COURSE
4. FIND THE 3 TERMS BETWEEN 13 AND -11.

14. THANK YOU!