# Jeff Bivin -- LZHS Arithmetic Sequences Last UpdatedApril 4, 2012.

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Jeff Bivin -- LZHS Arithmetic Sequences Last UpdatedApril 4, 2012

Arithmetic Sequences 5, 8, 11, 14, 17, 20, … 3n+2, … -4, 1, 6, 11, 16, … 5n – 9,... 11, 7, 3, -1, -5, … -4n + 15,...

General term or n th term of an arithmetic sequence a n = a 1 + (n – 1)d

Find the general term of an arithmetic sequence First term is 8 Common difference is 3 a n = a 1 + (n – 1)d a n = 8 + (n – 1)3 a n = 8 + 3n – 3 a n = 3n + 5

Find the general term First term is 23 Common difference is -4 a n = a 1 + (n – 1)d a n = 23 +(n – 1)(-4) a n = 23 - 4n + 4 a n = -4n + 27

Find the 100 th term 5, 11, 17, 23, 29,... a n = a 1 + (n – 1)d a 100 = 5 + (100 – 1)6 a 100 = 5 + 6(99) a 100 = 5 + 594 a 100 = 599 a 1 = 5 d = 6 n = 100

Find the general term and a recursive formula 4th term: 108 956 th term: -15124 108 = a 1 + 3d -15124 = a 1 + 955d So…. d = -16 and a 1 = 156 General term:Recursive formula: a n = 156 +(n-1)(-16) a n = a n-1 -16 a n = -16n + 172

Summing it up (adding the terms of an arithmetic sequence)

Find the sum of the first 7 terms: 1, 4, 7, 10, 13, 16, 19, … a 1 = 1 a n = 19 n = 7

Find the sum of the first 5 terms and the first n terms. 1, 3, 5, 7, 9, …2n-1

Find the sum of the integers from 1 to 100 a 1 = 1 a n = 100 n = 100

Find the sum: 8+11+14+17…+ (3n+5) a 1 = 8 a n = 3n+5 Jeff Bivin -- LZHS Find the sum of the first 20 terms: OR

Find the sum: 5 + 9 + 13 + … + 49 a 1 = 5 a n = 49 d = 4 n = ?

Find the sum: 13 + 15 + 17 +…+ 47 a 1 = 13 a n = 47 d = 2 n = ?

Evaluate a 1 = -29 a n = -199 d = -2 n = 86 S n = -29 - 31 - 33 +... - 199

Review – Arithmetic Sequences n th term Sum of n terms

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