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1. Consider the infinite arithmetic sequence $A$ with first term $5$ and common difference $-2$. Now define the infinite sequence $B$ so that the $k^{th}$ term of $B$ is $2$ raised to the $k^{th}$ term of $A$. Find the sum of all of the terms of $B$.

2. The terms $140, a, \frac{45}{28}$ are the first, second and third terms, respectively, of a geometric sequence. If $a$ is positive, what is the value of $a$?

 May 8, 2018
 #1
avatar+27531 
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"1. Consider the infinite arithmetic sequence $A$ with first term $5$ and common difference $-2$. Now define the infinite sequence $B$ so that the $k^{th}$ term of $B$ is $2$ raised to the $k^{th}$ term of $A$. Find the sum of all of the terms of $B$."

 

.

 May 8, 2018
 #2
avatar+27531 
+1

"2. The terms $140, a, \frac{45}{28}$ are the first, second and third terms, respectively, of a geometric sequence. If $a$ is positive, what is the value of $a$?"

 

 May 8, 2018
 #3
avatar+21826 
0

2. The terms $140, a, \frac{45}{28}$ are the first, second and third terms, respectively, of a geometric sequence. If $a$ is positive, what is the value of $a$?

 

 

\(\begin{array}{|rcll|} \hline a &=& \sqrt{140\cdot \frac{45}{28}} \\ a &=& 15 \\ \hline \end{array}\)

 

laugh

 May 8, 2018

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