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Worksheet for Sequence & Series (Unit 1C) PowerPoint: Definition: An __________________ ________________ is a sequence of numbers that has a ___________ difference between every two consecutive terms. o Example: ___________________________ o Constant difference means each successive number ___________ or ___________ by the ___________ amount. Definition: An ________________ _____________ is the _____________ of the terms in an arithmetic sequence. o Example: ___________________________ (Arithmetic Sequence) o Example: ___________________________ (Arithmetic Series) To find the EXACT term in arithmetic sequence, use the ____________ formula. o Explicit Formula is an = _______________________ o You must fill in the constant difference which is the _____ in the formula. o You must fill in the 1st term which is _______ in the formula. o In the following sequence: 5, 11, 17, 23,…. d = _______, and a 1 = __________ Try again: Given Sequence 15, 13, 11, 9… d - ______, a1 = _______, explicit formula for this sequence is ___________________ Use the explicit formula to find the 50th term a50 = ___ (____ - ____) + _____ = ______ Try again: Given Sequence 50, 40.5, 41, 36.5 … d - ______, a1 = _______, explicit formula for this sequence is ___________________ Use the explicit formula to find the 25th term a25 = ___ (____ - ____) + _____ = ______ Pyramid Problem: _____ + _____ + ______ + ………..…. + _____ + ______ + ______ (list seq. forwards) _____ + _____ + ______ + ………..…. + _____ + ______ + ______ (list seq. backwards) _____ + _____ + ______ + ……… (Sum each pair created) _____________________=10,100_ But this answer is too large…Why? _____________ _____________________= 5,050_ We need to ½ our answer, so _______ by 2. Activity 1: (Look back at last example and do the same thing with your new sequence) Activity 2: (This one may take just a bit longer! THINK, and look at Hint on the screen!) What is our NEW formula to SUM a sequence? Sn = ____ ( ______ + ______) where n = _______________________________ And a1 = _______________________________ And an = ________________________________ REMEMBER: IF YOUR WORKSHEET TODAY doesn’t give you the last term in the sequence, you must use the Explicit Formula an = d(n – 1) + a1 to calculate the last term in the sequence, before you can plug all values into the Sn formula. Student Practice: 𝒏 Use the Arithmetic Sum Formula to complete each problem below: Sn = 1) Given the following arithmetic series, find the sum of the series: 1 + 2 + 3 + 4 + … + 999 + 1000 𝟐 (𝒂𝟏 + 𝒂𝒏 ) 2) Given the following arithmetic series, find the sum of the series: 2 + 4 + 6 + 8 + … + 598 + 600