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what is a possible value for the missing term of the geometric sequence? 35,____,875,...

 Jul 9, 2015

Best Answer 

 #1
avatar+25325 
+5

what is a possible value for the missing term of the geometric sequence? 35,____,875,...

 

$$\small{\text{$
\boxed{~~ a_n=a_1\cdot r^{n-1}~~}
$}}\\\\
\small{\text{$
\begin{array}{rclcl}
a_1 &=& 35\\\\
a_2 &=& 35\cdot r\\\\
a_3 &=& 35\cdot r^2 &=& 875\\\\
&& 35\cdot r^2 &=& 875\\\\
&& r^2 &=& \dfrac{875}{35}\\\\
&& r^2 &=& 25\\\\
&& r^2 &=& 25 \qquad | \qquad \sqrt{}\\\\
&& r &=& \pm5 \\\\
a_2 &=& 35\cdot (\pm 5)\\
&&&& a_2 = 175 \qquad \text{ or }\qquad a_2 = -175
\end{array}
$}}$$

 

 Jul 9, 2015
 #1
avatar+25325 
+5
Best Answer

what is a possible value for the missing term of the geometric sequence? 35,____,875,...

 

$$\small{\text{$
\boxed{~~ a_n=a_1\cdot r^{n-1}~~}
$}}\\\\
\small{\text{$
\begin{array}{rclcl}
a_1 &=& 35\\\\
a_2 &=& 35\cdot r\\\\
a_3 &=& 35\cdot r^2 &=& 875\\\\
&& 35\cdot r^2 &=& 875\\\\
&& r^2 &=& \dfrac{875}{35}\\\\
&& r^2 &=& 25\\\\
&& r^2 &=& 25 \qquad | \qquad \sqrt{}\\\\
&& r &=& \pm5 \\\\
a_2 &=& 35\cdot (\pm 5)\\
&&&& a_2 = 175 \qquad \text{ or }\qquad a_2 = -175
\end{array}
$}}$$

 

heureka Jul 9, 2015

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