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 12:50, 20 May 2015

Question Find the sum

Step 1:
This is the sum of an arithmetic sequence. The common difference is Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle d=4} . Since the formula for an arithmetic sequence is
Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle a_{n}=a_{1}+d(n-1)} , the formula for this arithmetic sequence is Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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 (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle a_{n}=49} in the formula above and solve for .
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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