ADVANCED ALG/TRIG Chapter 11 – Sequences and Series.

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Presentation transcript:

ADVANCED ALG/TRIG Chapter 11 – Sequences and Series

icic ADVANCED ALG/TRIG Chapter 11 – Sequences and Series Sequences (an ordered list of numbers)

GeometricGeometric ADVANCED ALG/TRIG Chapter 11 – Sequences and Series Sequences (an ordered list of numbers) Series (sum of terms in a sequence)

GeometricGeometric ADVANCED ALG/TRIG Chapter 11 – Sequences and Series Sequences (an ordered list of numbers) Arithmetic D = common difference Arithmetic mean = sum of 2 numbers divided by 2 (the average) Series (sum of terms in a sequence)

GeometricGeometric ADVANCED ALG/TRIG Chapter 11 – Sequences and Series Sequences (an ordered list of numbers) Arithmetic D = common difference Arithmetic mean = sum of 2 numbers divided by 2 (the average) Recursive formula a n = a n-1 + d; a 1 given Explicit formula a n = a 1 + (n-1)d Series (sum of terms in a sequence)

GeometricGeometric ADVANCED ALG/TRIG Chapter 11 – Sequences and Series Sequences (an ordered list of numbers) Geometric R = common ratio Geometric mean = square root of product of 2 numbers Arithmetic D = common difference Arithmetic mean = sum of 2 numbers divided by 2 (the average) Recursive formula a n = a n-1 + d; a 1 given Explicit formula a n = a 1 + (n-1)d Series (sum of terms in a sequence)

GeometricGeometric ADVANCED ALG/TRIG Chapter 11 – Sequences and Series Sequences (an ordered list of numbers) Geometric R = common ratio Geometric mean = square root of product of 2 numbers Recursive formula a n = a n-1  r; a 1 given Explicit formula a n = a 1  r (n-1) Arithmetic D = common difference Arithmetic mean = sum of 2 numbers divided by 2 (the average) Recursive formula a n = a n-1 + d; a 1 given Explicit formula a n = a 1 + (n-1)d Series (sum of terms in a sequence)

GeometricGeometric ADVANCED ALG/TRIG Chapter 11 – Sequences and Series Sequences (an ordered list of numbers) Geometric R = common ratio Geometric mean = square root of product of 2 numbers Recursive formula a n = a n-1  r; a 1 given Explicit formula a n = a 1  r (n-1) Arithmetic D = common difference Arithmetic mean = sum of 2 numbers divided by 2 (the average) Recursive formula a n = a n-1 + d; a 1 given Explicit formula a n = a 1 + (n-1)d Series (sum of terms in a sequence) Arithmetic Finite – ends Infinite – does not end… Summation Notation uses Sigma  ; has lower and upper limits

GeometricGeometric ADVANCED ALG/TRIG Chapter 11 – Sequences and Series Sequences (an ordered list of numbers) Geometric R = common ratio Geometric mean = square root of product of 2 numbers Recursive formula a n = a n-1  r; a 1 given Explicit formula a n = a 1  r (n-1) Arithmetic D = common difference Arithmetic mean = sum of 2 numbers divided by 2 (the average) Recursive formula a n = a n-1 + d; a 1 given Explicit formula a n = a 1 + (n-1)d Series (sum of terms in a sequence) Arithmetic Finite – ends Infinite – does not end… Summation Notation uses Sigma  ; has lower and upper limits Sum of a Finite Arithmetic Series S = n/2(a 1 + a n )

GeometricGeometric ADVANCED ALG/TRIG Chapter 11 – Sequences and Series Sequences (an ordered list of numbers) Geometric R = common ratio Geometric mean = square root of product of 2 numbers Recursive formula a n = a n-1  r; a 1 given Explicit formula a n = a 1  r (n-1) Arithmetic D = common difference Arithmetic mean = sum of 2 numbers divided by 2 (the average) Recursive formula a n = a n-1 + d; a 1 given Explicit formula a n = a 1 + (n-1)d Series (sum of terms in a sequence) Geometric FINITE – ends; has a sum INFINITE Converges when |r|<1; approaches a limit Diverges when |r|> 1; does not approach a limit Arithmetic Finite – ends Infinite – does not end… Summation Notation uses Sigma  ; has lower and upper limits Sum of a Finite Arithmetic Series S = n/2(a 1 + a n )

GeometricGeometric ADVANCED ALG/TRIG Chapter 11 – Sequences and Series Sequences (an ordered list of numbers) Geometric R = common ratio Geometric mean = square root of product of 2 numbers Recursive formula a n = a n-1  r; a 1 given Explicit formula a n = a 1  r (n-1) Arithmetic D = common difference Arithmetic mean = sum of 2 numbers divided by 2 (the average) Recursive formula a n = a n-1 + d; a 1 given Explicit formula a n = a 1 + (n-1)d Series (sum of terms in a sequence) Geometric FINITE – ends; has a sum INFINITE Converges when |r|<1; approaches a limit Diverges when |r|> 1; does not approach a limit Sum of a Finite Geometric Series S n = a 1 (1-r n ) 1 - r Sum of an Infinite Geometric Series S n = a r Arithmetic Finite – ends Infinite – does not end… Summation Notation uses Sigma  ; has lower and upper limits Sum of a Finite Arithmetic Series S = n/2(a 1 + a n )