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For the following sequence: 9, 13, 17, 21, ... The rule for the nth term. an = Find: The common difference. The next three terms. The indicated term. a38 = in simplified form: (like an = 5+4n) Arithmetic Sequences & Series , add4 add4 , add4 Finding "the rule":an = a1 + (n-1)•dan = 9 + (n-1)•4 9 + 4n - 4an = 5 + 4n Finding a38:a38 = 5 + 4•(38)a38 = 5 + 152a38 = 157 this is simplified form For the following sequence: 18, 16, 14, 12, ... The rule for the nth term. an = Find: The common difference. The next three terms. The indicated term. a25 = in simplified form: (like an = 5+4n) Arithmetic Sequences & Series , sub2 sub2 , sub2 Finding "the rule":an = a1 + (n-1)•dan = 18 + (n-1)•-2 18 - 2n + 2an = 20 - 2n Finding a25:a25 = 20 - 2•(25)a25 = 20 - 50a25 = -30 this is simplified form For the following sequence: 21, 41, 61, 81, ... The rule for the nth term. an = Find: The common difference. The next three terms. The indicated term. a29 = in simplified form: (like an = 5+4n) Arithmetic Sequences & Series , , Finding "the rule":an = a1 + (n-1)•d For the following sequence: 26, 34, 42, 50, ... The rule for the nth term. an = Find: The common difference. The next three terms. The indicated term. a22 = in simplified form: (like an = 5+4n) Arithmetic Sequences & Series , , Finding "the rule":an = a1 + (n-1)•d For the following sequence: 33, 27, 21, 15, ... The rule for the nth term. an = Find: The common difference. The next three terms. The indicated term. a40 = in simplified form: (like an = 5+4n) Arithmetic Sequences & Series , , Finding "the rule":an = a1 + (n-1)•d For the following sequence: −31, −33, −35, −37, ... The rule for the nth term. an = Find: The common difference. The next three terms. The indicated term. a28 = in simplified form: (like an = 5+4n) Arithmetic Sequences & Series , , Finding "the rule":an = a1 + (n-1)•d For the following sequence: 38, 238, 438, 638, ... The rule for the nth term. an = Find: The common difference. The next three terms. The indicated term. a29 = 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 = 3 Find: The next three terms. Write the rule in simplified form:an = a1 + (n-1)•dan = 9 + (n-1)•3 in simplified form: (like an = 5+4n) Arithmetic Sequences & Series an = 9 + 3n - 3 an = 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 - 48 9 = a1 The rule for the nth term. an = Given: A term in an arithmetic sequence and the common difference. a14 = -136, d = -8 Find: The next three terms. Write the rule in simplified form:an = a1 + (n-1)•dan = -32 + (n-1)•-8 in simplified form: (like an = 5+4n) Arithmetic Sequences & Series an = -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. a21 = -128, d = -5 Find: 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. a31 = 104, d = 3 Find: The next three terms. in simplified form: (like an = 5+4n) Arithmetic Sequences & Series , , Find the sum if the first "n" terms of the indicated series. 4 + 8 + 12 + 16... n = 10 Identify a1: Find a10 = Use the sum formula to find the sum. = Arithmetic Sequences & Series 10•(4+40) 2 = 440 2 = 220 Finding "an":a10 = a1 + (n-1)•da10 = 4 + (10-1)•4 4 + (9)•4a10 = 40 Find the sum if the first "n" terms of the indicated series. 4 + 0 + (−4) + (−8)... n = 10 Identify a1: Find a10 = Use the sum formula to find the sum. Arithmetic Sequences & Series Finding "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 & Series This is an. Use it to find a1 & a10. Finding "a1":an = 2i + 4a1 = 2(1) + 4 = 6 Finding "a10":an = 2i + 4a10 = 2(10) + 4 = 24 Find a1 = Find a10 = Use the sum formula to find the sum. Find the sum of the series using summation notation. Arithmetic Sequences & Series This is an. Use it to find a1 & a7. |