arithmetic mean & arithmetic series

ARITHMETIC MEANARITHMETIC SERIES

ARITHMETIC MEAN

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

ARITHMETIC MEAN

Arithmetic Mean =

Formula

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

ARITHMETIC MEAN

•Use a6=a1+5d to solve for d.

25= 5+5d

5d=25-5

5d=20

d=4

Example 1

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

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

ARITHMETIC MEAN

Use a6=a1+5d to solve for d.

-4= -24+5d

5d=4-24

5d=-20

d=-4

Example 2

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

ARITHMETIC SERIES

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.

ARITHMETIC SERIES

Sn = (a1 + an)

Formulae

Sn = [2a1 + (n - 1) d]

ARITHMETIC SERIES

3 + 8 + 13 + … + 73

• a1 = 3

• an = 73

• d = 5• n = ?

• Sn = ?

Example 1

ARITHMETIC SERIES

Sn = (a1 + an)

S15 = (3 + 73)

S15 = (76)

S15 = (38)

S15 =

Example 1

ARITHMETIC SERIES

What is the sum of the first 10 terms in the series:3, 7, 11, …

• a1 = 3

•d = 4• n = 10

• an = ?

• Sn = ?

Example 2

ARITHMETIC SERIES

an = a1 + (n – 1) d

a10 = 3 + (10 – 1) 4

a10 = 3 + (9) 4

a10 = 3 + 36

a10 = 39

Example 2

ARITHMETIC SERIES

Sn = (a1 + an)

S10 = (3 + 39)

S10 = 5 (42)

S10 =

Example 2

ARITHMETIC MEANARITHMETIC SERIES