Grade X

IISYIISY

ARITHMETIC SEQUENCESARITHMETIC SEQUENCES

SutarmanSutarman20102010

Sequences and SeriesSequences and Series

SEQUENCES

SERIES

ARITHMETIC

GEOMETRIC

A sequence is a set of numbers listed in a certain order.

A series is the sum of the terms of a sequence.

Objectives & Minimum StandardObjectives & Minimum Standard

1.1. To find the To find the first termfirst term of Arithmetic of Arithmetic Sequences.Sequences.

2.2. To find the To find the common differencecommon difference of of Arithmetic Sequences.Arithmetic Sequences.

3.3. To find the To find the nnthth term term of Arithmetic of Arithmetic Sequences.Sequences.

MINIMUM STANDARD = 61

Dodi has to find two buildings to deliver packages:1. 91st building at the left side of Arjuna Street. 2. 62nd building at the left side of Arjuna Street.

Arjuna Street

1 3 5 7 9 11 13 . . .

2 4 6 8 10 . . .

?HELP!

!!

HELP!!!

HELP!!!

12

Dodi needs our help now!

1. What is the 91st building number at the left side of Arjuna Street?

2. What is the 62nd building number at the right side of Arjuna Street?

Can we help him?What do we need?FORMULA!

Wee need

In Mathematics, set of building numbers at both sides of Arjuna Street is called Arithmetic Sequence:(a) 1, 3, 5, 7, 9, 11, 13, …(b) 2, 4, 6, 8, 10, 12, …

Can you make another example of Arithmetic Sequence?

Definition Arithmetic Sequence (or

Arithmetic Progression) is a sequence of numbers such that, after the first number, each number is formed by adding a fixed number onto the preceding one.

The fixed number, denoted by d, is known as the common difference.

Each number in sequence is called a term, denoted by Tn.

Remember!

QUIZ 1

Which one of these sequences is Arithmetic Sequence?

(a) 3, 6, 9, 12, …

(b) 3, 9, 27, 81, …

In these Arithmetic Sequences, what is the number behind the question mark? Find the common difference (d) of each Arithmetic Sequence!

(a) 3 , 6 , 9 , 12 , 15 , 18 , 21, … d = 6 - 3 = 3

(b) 1 , 5 , 9 , 13 , 17 , 21 , 25 , … d = 5 - 1 = 4

QUIZ 2

? ? ?? ?

Do you remember Dodi’s problem?We need a formula to help him!

Look at this Arithmetic Sequence!

2, 4, 6, 8, 10, 12, … ?

T1, T2, T3, T4, T5, T6, … Tn a = T1 is called first term

Tn is called nth termd = Tn – T(n-1) is called common difference

T1 = a

= a + 2dT3 = T2 + d

= a + d

T2 = T1 + d

T1,

To Find the Formula

T2,

+d

T3,

+d

= (a + d ) + d

+d

T4, … ,Tn

..

Answer:The sequence at the left side of Arjuna Street is1, 3, 5, 7, 9, 11, 13, …a = 1, d = 2 , n = 91 (91st building)Tn = a + (n -1)d T91 = 1 + (91-1)(2) = 1 + 90(2) = 1 + 180

= 181So, the 91st building number is 181. Now, Dodi can go directly to the building number

181.

1. What is the 91st building number at the left side of Arjuna Street?

It’s time to help Dodi!

It’s time to help Dodi!

Can you help Dodi to find the 62nd building number at the right side of Arjuna Street?2, 4, 6, 8, 10, 12, …

ExerciseFind the first term, common difference and the nth term asked for each of the following Arithmetic Sequence!

(a) 3, 7, 11, 15, … T10 = …

(b)-15, -20, -25, -30, … T26 = …

• Terima kasih• Thank you

•Kye zu tin ba de