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2015-06-01T05:47:59Z

Created page with "<span class="exam"> Given a sequence <math>10, 7, 4, 1, \ldots</math> use formulae on the back page to compute <math>S_{20}</math> {| class="mw-collapsible mw-collapsed" style..."

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<span class="exam"> Given a sequence <math>10, 7, 4, 1, \ldots</math> use formulae on the back page to compute <math>S_{20}</math>
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Foundations
|-
|1) What is the formula for the nth term of an arithmetic sequence?
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|2) What is the formula for the sum of the first n terms of an arithmetic sequence?
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|Answer:
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|1) The nth term of an arithmetic sequence is <math>A_n=A_1+d(n-1)</math> where <math>A_1</math> is the first term of the sequence and <math>d</math> is the common difference.
|-
|2) The sum of the first n terms of an arithmetic sequence is <math> S_n=\frac{n}{2}(A_1+A_n)</math>.
|}

Solution:

{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
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|The first term in the arithmetic sequence is <math> A_1=10</math> and the common difference is <math>d=-3</math>.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
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|The 20th term of this sequence is <math>A_{20}=10+-3(20-1)=10-3(19)=10-57=-47</math>.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 3:
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|The sum of the first twenty terms is <math>S_{20}=\frac{20}{2}(10+-47)=10(-37)=-370</math>.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer:
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|<math>-370</math>
|}

[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

004 Sample Final A, Problem 7 - Revision history

MathAdmin: Created page with " Given a sequence 10, 7, 4, 1, \ldots use formulae on the back page to compute S_{20} {| class="mw-collapsible mw-collapsed" style..."

MathAdmin: Created page with " Given a sequence $10, 7, 4, 1, \ldots$ use formulae on the back page to compute $S_{20}$ {| class="mw-collapsible mw-collapsed" style..."