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Transcript
9.1 Series and Sequences Understand NOTATIONToday is a language of asking you to find terms in patterns List the next three numbers 4, 10, 16, 22… 1, 4, 9, 16, … 1, 1, 2, 3, 5, 8, 13… Vocabulary • Sequence- A list of numbers that may or may not be in a pattern; a function whose domain is a set of positive integers (whole numbers) • Term- a number in the sequence NOTATION: an is an identified sequence n stands for the term number/position Example an= 3n -2 Example a1 = 3(1)-2 = 1 Example a2 = 3(2)-2 = 4 … Thus an= 1, 4, 7, 10,… Examples Page 621 # 3 an = 2n Find the first five terms of the sequence (Meditate and let notation sink in) Vocabulary • Infinite sequence- The set of all terms in a sequence; Goes on forever with no end a1 , a2 , a3 , …, an , … • Finite sequence- If the set includes only up to a set/fixed/finite nth term; Ends a4 , a5 , a6 , …, an Recursive Sequence • Recursive Sequence- A sequence in which previous term(s) are NEEDED to find the next Example of finding a recursive sequence #55 a1 =28 ak+1 =ak - 4 Write the recursive sequence/function for Fibonacci Sequence 1,1,2,3,5,8, … Factorials!!! • Notated by n! (read n factorial) • The factorial of a non-negative integer n is the product of all positive integers (whole numbers) less than and equal to n. 5!= 5•4•3•2•1 = 120 Find ! on your calculator!!! Evaluating Factorials Coming up with shortcuts • #63 4!/6! • #68 (n+2)!/n! Homework: • 9.1Page 621 • #s 2-5; 7-13(odd); 25-27; 31; 55-57; try 59&60; 63-69