005 Sample Final A, Question 21 - Revision history

Matt Lee at 04:15, 22 May 2015

2015-05-22T04:15:08Z

Kayla Murray at 19:50, 20 May 2015

2015-05-20T19:50:21Z

Kayla Murray at 19:21, 20 May 2015

2015-05-20T19:21:02Z

Matt Lee: Created page with "''' Question''' Find the sum
$5 + 9 + 13 + \cdots + 49$ {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Final Answers |..."

2015-05-01T04:11:41Z

Created page with "''' Question''' Find the sum <br> <center><math> 5 + 9 + 13 + \cdots + 49 </math></center> {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Final Answers |..."

New page

''' Question''' Find the sum <br>
<center><math> 5 + 9 + 13 + \cdots + 49 </math></center>

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answers
|-
|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, <math>a_n = (-a)^n</math>
|-
|b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
|-
|c) False. <math>y = x^2</math> does not have an inverse.
|-
|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
|-
|e) True.
|-
|f) False.
|}

@@ Line 5: / Line 5: @@
 ! Step 1:
 |-
+|This is the sum of an arithmetic sequence. The common difference is <math>d=4</math>. Since the formula for an arithmetic sequence is
 |}
@@ Line 11: / Line 13: @@
 ! Step 2:
 |-
+| We need to figure out how many terms we are adding together. To do this, we let <math>a_n=49</math> in the formula above and solve for <math>n</math>.
 |}
@@ Line 17: / Line 19: @@
 ! Step 3:
 |-
+| If <math>49=5+4(n-1)</math>, we have <math>44=4(n-1)</math>. Dividing by 4, we get <math>11=n-1</math>. Therefore, <math>n=12</math>.
 |}
@@ Line 25: / Line 25: @@
 ! Step 4:
 |-
+|The formula for the sum of the first n terms of an arithmetic sequence is <math>S_n=\frac{1}{2}n(a_1+a_n)</math>.
 |}
@@ Line 31: / Line 31: @@
 ! Step 5:
 |-
+|Since we are adding 12 terms together, we want to find <math>S_{12}</math>. So, <math>S_{12}=\frac{1}{2}(12)(5+49)=324</math>.
 |}
@@ Line 41: / Line 37: @@
 ! Final Answer:
 |-
+| 324
 |}

@@ Line 1: / Line 1: @@
 ''' Question''' Find the sum <br>
 <center><math> 5 + 9 + 13 + \cdots + 49 </math></center>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"

@@ Line 3: / Line 3: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Final Answers
+! Step 1:
 |-
-|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, <math>a_n = (-a)^n</math>
 |-
-|b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
 |-
-|c) False. <math>y = x^2</math> does not have an inverse.
 |-
-|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
 |-
-|e) True.
 |-
-|f) False.
 |}

005 Sample Final A, Question 21 - Revision history

Matt Lee at 04:15, 22 May 2015

Kayla Murray at 19:50, 20 May 2015

Kayla Murray at 19:21, 20 May 2015

Matt Lee: Created page with "''' Question''' Find the sum 5 + 9 + 13 + \cdots + 49 {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Final Answers |..."

Matt Lee: Created page with "''' Question''' Find the sum
$5 + 9 + 13 + \cdots + 49$ {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Final Answers |..."