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ARITHMETIC SEQUENCES

IISY. IISY. ARITHMETIC SEQUENCES. Grade X. Sutarman. 2010. Sequences and Series. SEQUENCES. ARITHMETIC. SERIES. 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 Standard.

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ARITHMETIC SEQUENCES

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  1. IISY IISY ARITHMETIC SEQUENCES Grade X Sutarman 2010

  2. Sequences and Series SEQUENCES ARITHMETIC SERIES GEOMETRIC A sequence is a set of numbers listed in a certain order. A series is the sum of the terms of a sequence.

  3. Objectives & Minimum Standard • To find the first term of Arithmetic Sequences. • To find the common difference of Arithmetic Sequences. • To find the nth term of Arithmetic Sequences. MINIMUM STANDARD = 61

  4. Dodi has to find two buildings to deliver packages:1. 91stbuilding at the left side of Arjuna Street. 2. 62nd building at the left side of Arjuna Street. HELP!!! HELP!!! ? 1 3 5 7 9 11 13 . . . Arjuna Street 12 2 4 6 8 10 . . . HELP!!!

  5. 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? Wee need Can we help him? What do we need? FORMULA!

  6. 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?

  7. Definition Remember! • 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.

  8. QUIZ 1 • Which one of these sequences is Arithmetic Sequence? • 3, 6, 9, 12, … • 3, 9, 27, 81, …

  9. QUIZ 2 • In these Arithmetic Sequences, what is the number behind the question mark? Find the common difference (d) of each Arithmetic Sequence! • 3 , 6 , 9 , 12 , 15 , 18 , 21, … d = 6 - 3 = 3 • 1 , 5 , 9 , 13 , 17 , 21 , 25 , … d = 5 - 1 = 4 ? ? ? ? ?

  10. 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 term d = Tn – T(n-1) is called common difference

  11. To Find the Formula +d +d +d T1, T2, T3, T4, … , Tn T1=a T2=T1+d =a + d T3=T2+d =(a + d )+ d =a +2d . .

  12. It’s time to help Dodi! 1. What is the 91st building number at the left side of Arjuna Street? Answer: The sequence at the left side of Arjuna Street is 1, 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 = 181 So, the 91st building number is 181. Now, Dodi can go directly to the building number 181.

  13. 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, …

  14. Exercise • Find the first term, common difference and the nth term asked for each of the following Arithmetic Sequence! • 3, 7, 11, 15, … T10= … • -15, -20, -25, -30, … T26= …

  15. Terima kasih • Thank you • Kye zu tin ba de

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