Worksheet for Sequence & Series (Unit 1C) PowerPoint:
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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.
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Definition: An ________________ _____________ is the _____________ of the terms
in an arithmetic sequence.
o Example: ___________________________ (Arithmetic Sequence)
o Example: ___________________________ (Arithmetic Series)
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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 = __________
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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 = ___ (____ - ____) + _____ = ______
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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 = ___ (____ - ____) + _____ = ______
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Pyramid Problem:
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_____ + _____ + ______ + ………..…. + _____ + ______ + ______ (list seq. forwards)
_____ + _____ + ______ + ………..…. + _____ + ______ + ______ (list seq. backwards)
_____ + _____ + ______ + ………
(Sum each pair created)
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_____________________=10,100_ But this answer is too large…Why? _____________
_____________________= 5,050_ We need to ½ our answer, so _______ by 2.
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Activity 1: (Look back at last example and do the same thing with your new sequence)
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Activity 2: (This one may take just a bit longer! THINK, and look at Hint on the screen!)
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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:
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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
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(𝒂𝟏 + 𝒂𝒏 )
2) Given the following arithmetic series, find the sum of the series: 2 + 4 + 6 + 8 + … + 598 + 600