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SEQUENCES

SEQUENCES. Unit Standard 5248. Starter. Write down the next three terms in the following sequences:- 2, 4, 6, 8, …, …, …. 3, 6, 12, 24, …, …, … 12, 7, 2, -3, …, …, … 8, 4, 2, 1, …, …, … 1, 3, 6, 10, …, …, … 2, -2, 2, -2, …, …, …. Definition.

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SEQUENCES

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  1. SEQUENCES Unit Standard 5248

  2. Starter • Write down the next three terms in the following sequences:- • 2, 4, 6, 8, …, …, …. • 3, 6, 12, 24, …, …, … • 12, 7, 2, -3, …, …, … • 8, 4, 2, 1, …, …, … • 1, 3, 6, 10, …, …, … • 2, -2, 2, -2, …, …, …

  3. Definition • Simply speaking a sequence is an ordered list of numbers. • Every sequence has a first number, a second number, etc • For most sequences there is a rule which can tell us what each number should be. • The numbers in a sequence are known as terms.

  4. Arithmetic Sequences • An ARITHMETIC sequence is one where there is a common difference between terms. • Examples:- • 1, 2, 3, 4, ….. • 3, 5, 7, 9, …… • 10, 15, 20, 25, ….. • 0, 0.5, 1, 1.5, 2, 2.5, ….. • 3, 0, -3, -6, …… In each example, can you see what the common difference is?

  5. Notation • Any term in a sequence is written as tn, where the n refers to the position in the sequence. Eg:- t3 is the third term, t5 is the fifth term • The first term is also referred to as a ie a = t1

  6. Notation for an Arithmetic Sequence • In an arithmetic sequence the common difference is d. • Examples:- • 1, 4, 7, 10, …. a=1, d=3 • 10, 8, 6, 4, …. a=10, d=-2 • 5, 11, 17, 23, …. a=5, d=6 • 1.73, 1.87, 2.01, 2.15, a=1.73, d=0.14

  7. Given a and d list the first 5 terms. a=1, d=4 a=7, d=-6 a=-95, d=3 a=13, d=11 a=1.5, d=0.75 1, 5, 9, 13, 17 7, 1, -5, -11, -17 -95, -92, -89, -86, -83 13, 24, 35, 46, 57 1.5, 2.25, 3.0, 3.75, 4.5 Arithmetic sequence examples

  8. A formula for the terms of an Arithmetic sequence. • The first term of an arithmetic sequence is :- a • To get the second term add on the d. t2 = a + d • To get the third term add another d. t3 = a + d + d = a + 2d • The fourth term will be.. t4 = t3 +d = a + 2d + d = a + 3d

  9. General term for an Arithmetic Sequence • Any term in an arithmetic sequence can be found using the formula: tn = a + (n – 1)d • Example: If a = 5 and d = 2 then t100 = 5 + (100-1).2 = 203 • tn is known as the general term or the nth term of the sequence.

  10. Practice Examples • Theta Maths Page 105 (Green) Exercise 13.1 Do q2, q3, q5, q10, q11

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