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Help 4

NotSoSmart  Mar 8, 2018

Best Answer 

 #1
avatar+2294 
+1

4) The sequence is certainly arithmetic! Notice that \({\underbrace{13,}\underbrace{20,}\underbrace{27,}34,...}\\ +7+7+7\) . In other words, the common difference is 7.

 

5) This is another arithmetic sequence with a common difference of -7.

 

Remember that awesome formula that tells you the nth term of an arithmetic sequence? It's \(a_n=a_1+d(n-1)\) . Let's use it!

 

\(a_n=a_1+d(n-1)\\ a_{50}=5-7(50-1)\\ a_{50}=5-7*49\\ a_{50}=-338\)

 

6) The arithmetic mean is also the average. 

 

\(a_n=\frac{a_{n-1}+a_{n+1}}{2}\\ a_n=\frac{3.9+7.1}{2}\\ a_n=\frac{11}{2}\\ a_n=5.5\)

TheXSquaredFactor  Mar 8, 2018
 #1
avatar+2294 
+1
Best Answer

4) The sequence is certainly arithmetic! Notice that \({\underbrace{13,}\underbrace{20,}\underbrace{27,}34,...}\\ +7+7+7\) . In other words, the common difference is 7.

 

5) This is another arithmetic sequence with a common difference of -7.

 

Remember that awesome formula that tells you the nth term of an arithmetic sequence? It's \(a_n=a_1+d(n-1)\) . Let's use it!

 

\(a_n=a_1+d(n-1)\\ a_{50}=5-7(50-1)\\ a_{50}=5-7*49\\ a_{50}=-338\)

 

6) The arithmetic mean is also the average. 

 

\(a_n=\frac{a_{n-1}+a_{n+1}}{2}\\ a_n=\frac{3.9+7.1}{2}\\ a_n=\frac{11}{2}\\ a_n=5.5\)

TheXSquaredFactor  Mar 8, 2018

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