Arithmetic Sequences
 The common difference.Find:For the following sequence:  9,   13,   17,   21, ...The rule for the nth term.  an =The indicated term.  a38 =The next three terms.in simplified form:  (like an = 5+4n) Arithmetic Sequences & Series,add4add4,add4Finding "the rule":an = a1 + (n-1)•dan = 9 + (n-1)•4        9 + 4n - 4an = 5 + 4nthis is simplified formFinding a38:a38 = 5 + 4•(38)a38 = 5 + 152a38 = 157 The common difference.Find:For the following sequence: 18,  16,   14,   12, ...The rule for the nth term.  an =The indicated term.  a25 =The next three terms.in simplified form:  (like an = 5+4n) Arithmetic Sequences & Series,sub2sub2,sub2Finding "the rule":an = a1 + (n-1)•dan = 18 + (n-1)•-2        18 - 2n + 2an = 20 - 2nthis is simplified formFinding a25:a25 = 20 - 2•(25)a25 = 20 - 50a25 = -30 The common difference.Find:For the following sequence:  1,   7,   13,   19, ...The rule for the nth term.  an =The indicated term.  a28 =The next three terms.in simplified form:  (like an = 5+4n) Arithmetic Sequences & Series,,Finding "the rule":an = a1 + (n-1)•d The common difference.Find:For the following sequence:  −13,   −11,   −9,   −7, ...The rule for the nth term.  an =The indicated term.  a40 =The next three terms.in simplified form:  (like an = 5+4n) Arithmetic Sequences & Series,,Finding "the rule":an = a1 + (n-1)•d The common difference.Find:For the following sequence: 11,   15,   19,   23, ...The rule for the nth term.  an =The indicated term.  a40 =The next three terms.in simplified form:  (like an = 5+4n) Arithmetic Sequences & Series,,Finding "the rule":an = a1 + (n-1)•d The common difference.Find:For the following sequence: 6,   −2,   −10,   −18, ...The rule for the nth term.  an =The indicated term.  a29 =The next three terms.in simplified form:  (like an = 5+4n) Arithmetic Sequences & Series,,Finding "the rule":an = a1 + (n-1)•d The rule for the nth term.  an =Given: A term in an arithmetic sequence and the common difference.a17 = 57, d = 3Find:The next three terms.Write the rule in simplified form:an = a1 + (n-1)•dan = 9 + (n-1)•3in simplified form:  (like an = 5+4n) Arithmetic Sequences & Seriesan = 9 + 3n - 3an = 6 + 3n,,Finding "the rule":an = a1 + (n-1)•dFind a1 first  a17 = a1 + (n-1)•d  57 = a1 + (17-1)•3  57 = a1 + (16)•3  57 = a1 + 48-48          - 489 = a1 The rule for the nth term.  an =Given: A term in an arithmetic sequence and the common difference.a14 = -136, d = -8Find:The next three terms.Write the rule in simplified form:an = a1 + (n-1)•dan = -32 + (n-1)•-8in simplified form:  (like an = 5+4n) Arithmetic Sequences & Seriesan = -32 - 8n + 8an = -24 - 8n,,Finding "the rule":an = a1 + (n-1)•dFind a1 first  a14 = a1 + (n-1)•d-136 = a1 + (14-1)•-8-136 = a1 + (13)•-8-136 = a1 - 104+104         +104-32 = a1 The rule for the nth term.  an =Given: A term in an arithmetic sequence and the common difference.a15 = 272, d = 20Find:The next three terms.in simplified form:  (like an = 5+4n) Arithmetic Sequences & Series,, The rule for the nth term.  an =Given: A term in an arithmetic sequence and the common difference.a34 = 26, d = 2Find:The next three terms.in simplified form:  (like an = 5+4n) Arithmetic Sequences & Series,, The rule for the nth term.  an =Given: A term in an arithmetic sequence and the common difference.a26 = -66, d = -4Find:The next three terms.in simplified form:  (like an = 5+4n) Arithmetic Sequences & Series,, Find a10 =Identify a1:Find the sum if the first "n" terms of the indicated series.4 + 8 + 12 + 16...          n = 10Use the sum formula to find the sum.=Arithmetic Sequences & Series10•(4+40)2=4402=220Finding "an":a10 = a1 + (n-1)•da10 = 4 + (10-1)•4          4 + (9)•4a10 = 40 Find a12 =Identify a1:Find the sum if the first "n" terms of the indicated series.25 + 34 + 43 + 52...      n = 12Use the sum formula to find the sum.Arithmetic Sequences & SeriesFinding "an":an = a1 + (n-1)•d Find a1 =Find a10 =Use the sum formula to find the sum.Find the sum of the series using summation notation.Arithmetic Sequences & SeriesThis is an. Use it to find a1 & a10.Finding "a1":an = 2i + 4a1 = 2(1) + 4 = 6Finding "a10":an = 2i + 4a10 = 2(10) + 4 = 24 Find a1 =Find a7 =Use the sum formula to find the sum.Find the sum of the series using summation notation.Arithmetic Sequences & SeriesThis is an. Use it to find a1 & a7.
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