Arithmetic Sequences

The common difference. Find: For the following sequence: 9, 13, 17, 21, ... The rule for the n The indicated term. a The next three terms. in simplified form: (like a _{n} = 5+4n) Arithmetic Sequences & Series _{,}add4 add4 _{,}add4 aFinding "the rule":_{n} = a_{1} + (n-1)•da_{n} = 9 + (n-1)•4 9 + 4n - 4a_{n} = 5 + 4nthis is simplified form :aFinding a_{38}_{38} = 5 + 4•(38)a_{38} = 5 + 152a_{38} = 157The common difference. Find: For the following sequence: 18, 16, 14, 12, ... The rule for the n The indicated term. a The next three terms. in simplified form: (like a _{n} = 5+4n) Arithmetic Sequences & Series _{,}sub2 sub2 _{,}sub2 aFinding "the rule":_{n} = a_{1} + (n-1)•da_{n} = 18 + (n-1)•-2 18 - 2n + 2a_{n} = 20 - 2nthis is simplified form :aFinding a_{25}_{25} = 20 - 2•(25)a_{25} = 20 - 50a_{25} = -30The common difference. Find: For the following sequence: 1, 7, 13, 19, ... The rule for the n The indicated term. a The next three terms. in simplified form: (like a _{n} = 5+4n) Arithmetic Sequences & Series _{,}_{,}aFinding "the rule":_{n} = a_{1} + (n-1)•dThe common difference. Find: For the following sequence: −13, −11, −9, −7, ... The rule for the n The indicated term. a The next three terms. in simplified form: (like a _{n} = 5+4n) Arithmetic Sequences & Series _{,}_{,}aFinding "the rule":_{n} = a_{1} + (n-1)•dThe common difference. Find: For the following sequence: 11, 15, 19, 23, ... The rule for the n The indicated term. a The next three terms. in simplified form: (like a _{n} = 5+4n) Arithmetic Sequences & Series _{,}_{,}aFinding "the rule":_{n} = a_{1} + (n-1)•dThe common difference. Find: For the following sequence: 6, −2, −10, −18, ... The rule for the n The indicated term. a The next three terms. in simplified form: (like a _{n} = 5+4n) Arithmetic Sequences & Series _{,}_{,}aFinding "the rule":_{n} = a_{1} + (n-1)•dThe rule for the n Given: A term in an arithmetic sequence and the common difference. a Find: The next three terms. aWrite the rule in simplified form:_{n} = a_{1} + (n-1)•da_{n} = 9 + (n-1)•3in simplified form: (like a _{n} = 5+4n) Arithmetic Sequences & Series a _{n} = 9 + 3n - 3a _{n} = 6 + 3n_{,}_{,}aFinding "the rule":_{n} = a_{1} + (n-1)•d aFind a_{1} first_{17} = a_{1} + (n-1)•d 57 = a_{1} + (17-1)•3 57 = a_{1} + (16)•3 57 = a_{1} + 48-48 - 489 = a _{1}The rule for the n Given: A term in an arithmetic sequence and the common difference. a Find: The next three terms. aWrite the rule in simplified form:_{n} = a_{1} + (n-1)•da_{n} = -32 + (n-1)•-8in simplified form: (like a _{n} = 5+4n) Arithmetic Sequences & Series a _{n} = -32 - 8n + 8a_{n} = -24 - 8n_{,}_{,}aFinding "the rule":_{n} = a_{1} + (n-1)•d aFind a_{1} first_{14} = a_{1} + (n-1)•d-136 = a_{1} + (14-1)•-8-136 = a_{1} + (13)•-8-136 = a_{1} - 104+104 +104-32 = a _{1}The rule for the n Given: A term in an arithmetic sequence and the common difference. a Find: The next three terms. in simplified form: (like a _{n} = 5+4n) Arithmetic Sequences & Series _{,}_{,}The rule for the n Given: A term in an arithmetic sequence and the common difference. a Find: The next three terms. in simplified form: (like a _{n} = 5+4n) Arithmetic Sequences & Series _{,}_{,}The rule for the n Given: A term in an arithmetic sequence and the common difference. a Find: The next three terms. in simplified form: (like a _{n} = 5+4n) Arithmetic Sequences & Series _{,}_{,}Find a Identify a Find the sum if the first "n" terms of the indicated series. 4 + 8 + 12 + 16... n = 10 Use the sum formula to find the sum. = Arithmetic Sequences & Series 10•(4+40) 2 = 440 2 = 220 aFinding "a:_{n}"_{10} = a_{1} + (n-1)•da_{10} = 4 + (10-1)•4 4 + (9)•4a_{10} = 40Find a Identify a Find the sum if the first "n" terms of the indicated series. 25 + 34 + 43 + 52... n = 12 Use the sum formula to find the sum. Arithmetic Sequences & Series aFinding "a:_{n}"_{n} = a_{1} + (n-1)•dFind a Find a Use the sum formula to find the sum. Find the sum of the series using summation notation. Arithmetic Sequences & Series This is a _{n}. Use it to find a_{1} & a_{10}.aFinding "a:_{1}"_{n} = 2i + 4a_{1} = 2(1) + 4 = 6Finding "a:_{10}"a_{n} = 2i + 4a_{10} = 2(10) + 4 = 24Find a Find a Use the sum formula to find the sum. Find the sum of the series using summation notation. Arithmetic Sequences & Series This is a _{n}. Use it to find a_{1} & a_{7}. |

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