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seque nces and ARITHMETIC SEQUENCES

Sequences and Arithmetic Sequences

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Page 1: Sequences and Arithmetic Sequences

sequencesandARITHMETIC SEQUENCES

Page 2: Sequences and Arithmetic Sequences

-in mathematics, it is a string of objects, like numbers, that follow a particular pattern. The individual elements in a sequence are called terms.

SEQUENCE

Page 3: Sequences and Arithmetic Sequences

- is a list of things (usually numbers) that are in order.-some of the simplest sequences can be found in multiplication tables:

SEQUENCE

Page 4: Sequences and Arithmetic Sequences

examples3, 6, 9, 12, 15, 18, 21, …

Pattern: “add 3 to the previous number to get the next number”0, 12, 24, 36, 48, 60, 72, …Pattern: “add 12 to the previous number to get the next number”

Page 5: Sequences and Arithmetic Sequences

examples10,–2 8,×2 16,–2 14,×2 28,–2 26,×2 52,

…Pattern: “alternatingly subtract 2 and multiply by 2 to get the next number”0,+2 2,+4 6,+6 12,+8 20,+10 30,+12 42, …Pattern: “add increasing even numbers to get the next number”

Page 6: Sequences and Arithmetic Sequences

infiniteSEQUENCE

When the sequence goes on forever it is called an infinite sequence,

otherwise it is a finite sequence

Page 7: Sequences and Arithmetic Sequences

examples{1, 2, 3, 4, ...} is a very simple sequence

(and it is an infinite sequence){20, 25, 30, 35, ...} is also an infinite sequence{1, 3, 5, 7} is the sequence of the first 4 odd numbers (and is a finite sequence)

Page 8: Sequences and Arithmetic Sequences

examples{1, 2, 4, 8, 16, 32, ...} is an infinite

sequence where every term doubles{a, b, c, d, e} is the sequence of the first 5 letters alphabetically

Page 9: Sequences and Arithmetic Sequences

arithmeticSEQUENCE

In an arithmetic sequence, the difference between consecutive terms is constant. The constant difference is denoted by d.

Page 10: Sequences and Arithmetic Sequences

arithmeticSEQUENCE

FORMULA: an= a1 + (n-1) d

Page 11: Sequences and Arithmetic Sequences

examples

Page 12: Sequences and Arithmetic Sequences

examples

Page 13: Sequences and Arithmetic Sequences

examples

Page 14: Sequences and Arithmetic Sequences

examplesFind the common difference and the

next term of the following sequence:3, 11, 19, 27, 35,...

Page 15: Sequences and Arithmetic Sequences

examples

To find the common difference, you have to subtract a pair of terms. It doesn't matter which

pair you pick, as long as they are right next to each other:

11 – 3 = 819 – 11 = 827 – 19 = 835 – 27 = 8

The difference is always 8, so d = 8. Then the next term is 35 + 8 = 43.

Page 16: Sequences and Arithmetic Sequences

examplesFind the common ratio and the

seventh term of the following sequence:

 2/9, 2/3, 2, 6, 18,...

Page 17: Sequences and Arithmetic Sequences

examplesTo find the common ratio, you have to divide a

pair of terms. It doesn't matter which pair you pick, as long as they're right next to each other:The ratio is always 3, so r = 3. Then the sixth

term is (18)(3) = 54 and the seventh term is(54)(3) = 162.

Page 18: Sequences and Arithmetic Sequences

examplesMarvin is practicing the guitar for a

competition. He starts by practicing the guitar for 30 minutes on the first day and

then increases the practice time by 10 minutes each day. If the pattern continues, how many minutes will he spend practicing

on the 7th day?

Page 19: Sequences and Arithmetic Sequences

examplesa1 = 30 minutes

d= 10 minutesa7 = ?

Page 20: Sequences and Arithmetic Sequences

examplesFORMULA: a7= 30 + (7-1)

10= 30 + 60

= 90 minutes

Page 21: Sequences and Arithmetic Sequences

examplesEd Sheeran’s concert venue has 100

rows of seats with 30 seats in the first row, 35 seats in the second row, 40

seats in the third row and so on. How many seats are there in the 69th row?

Page 22: Sequences and Arithmetic Sequences

examplesa1 = 30 seats

d= 5 seatsa69 = ?

Page 23: Sequences and Arithmetic Sequences

examplesFORMULA: a69= 30 + (69-1)

5= 30 + 340

= 370 seats

Page 24: Sequences and Arithmetic Sequences

Prepared by:- Daphne Millen Arenas

-Kent Daryl Acuna-Marvin Dale Lopez

- Angelicka Kim Batalla- Ericka Lei Gamalong