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A geometric sequence of positive integers is formed for which the first term is 3 and the fourth term is 192. What is the third term of the sequence?

 Jan 26, 2015

Best Answer 

 #1
avatar+26400 
+10

$$\small{\text{Geometric sequence :
$ a_1=a,\ a_2=a*r,\ a_3=a*r^2,\ a_4=a*r^3,\ a_5=a*r^4,\ \dots $
}}\\
\small{\text{
$ a_1=a=3 \qquad a = 3 $
}}\\
\small{\text{
$ a_4=a*r^3 = 3*r^3 =192 \qquad 3*r^3 =192 \qquad r^3 =64 \qquad r =4 $
}}\\
\small{\text{
$ a_3=a*r^2 = 3*4^2 = 3*16 = 48$
}}$$

.
 Jan 27, 2015
 #1
avatar+26400 
+10
Best Answer

$$\small{\text{Geometric sequence :
$ a_1=a,\ a_2=a*r,\ a_3=a*r^2,\ a_4=a*r^3,\ a_5=a*r^4,\ \dots $
}}\\
\small{\text{
$ a_1=a=3 \qquad a = 3 $
}}\\
\small{\text{
$ a_4=a*r^3 = 3*r^3 =192 \qquad 3*r^3 =192 \qquad r^3 =64 \qquad r =4 $
}}\\
\small{\text{
$ a_3=a*r^2 = 3*4^2 = 3*16 = 48$
}}$$

heureka Jan 27, 2015

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