3. ARITHMETIC MEAN
Finding a certain number of terms between two given
terms of an arithmetic sequence
The terms between any two nonconsecutive terms of
an arithmetic sequence are known as arithmetic
means
5. ARITHMETIC MEAN
Insert 4 arithmetic means between 5 and 25.
• Since we are required to insert 4 terms, then there will be 6 terms in all.
• Let a1=5 and a6=25, we will insert a2, a3, a4, a5 as shown below.
5, a2, a3, a4, a5, 25
Example 1
7. ARITHMETIC MEAN
Using the value of d, we can now get the values of a2, a3, a4, a5, thus:
a2=9, a3=13, a4=17, a5=21
Example 1
5, 9, 13, 17, 21, 25
8. ARITHMETIC MEAN
Insert 4 arithmetic means between -24 and -4.
• Since we are required to insert 4 terms, then there will be 6 terms in all.
• Let a1=-24 and a6=-4, we will insert a2, a3, a4, a5 as shown below.
-24, a2, a3, a4, a5, -4
Example 2
10. ARITHMETIC MEAN
Using the value of d, we can now get the values of a2, a3, a4, a5, thus:
a2=-20, a3=-16, a4=-12, a5=-8
Example 2
-24, -20, -16, -12, -8, -4
12. ARITHMETIC SERIES
It is the sum of an arithmetic sequence
The sum of an arithmetic series is found by multiplying
the number of terms times the average of the first and
last terms.