Difference between revisions of "005 Sample Final A, Question 21"

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|This is the sum of an arithmetic sequence. The common difference is <math>d=4</math>. Since the formula for an arithmetic sequence is
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|<math>a_n=a_1+d(n-1)</math>, the formula for this arithmetic sequence is <math>a_n=5+4(n-1)</math>.
 
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| 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>.
 
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| 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>.
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|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>.
 
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|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>.
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Revision as of 11:50, 20 May 2015

Question Find the sum

Step 1:
This is the sum of an arithmetic sequence. The common difference is . Since the formula for an arithmetic sequence is
, the formula for this arithmetic sequence is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_n=5+4(n-1)} .
Step 2:
We need to figure out how many terms we are adding together. To do this, we let Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_n=49} in the formula above and solve for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} .
Step 3:
If Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 49=5+4(n-1)} , we have Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 44=4(n-1)} . Dividing by 4, we get Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 11=n-1} . Therefore, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n=12} .
Step 4:
The formula for the sum of the first n terms of an arithmetic sequence is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S_n=\frac{1}{2}n(a_1+a_n)} .
Step 5:
Since we are adding 12 terms together, we want to find Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S_{12}} . So, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S_{12}=\frac{1}{2}(12)(5+49)=324} .
Final Answer:
324
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