Answer:
[tex]a_n= 64 \times (\frac{3}{4})^{n-1}[/tex]
Step-by-step explanation:
A bouncing toy reaches a height of 64 inches at its first peak.
A bouncing toy reaches a height of 48 inches at its second peak.
A bouncing toy reaches a height of 36 inches at its third peak.
So, the sequence becomes : 64, 48,36 ....
So, a = first term = 64
r = common ratio = [tex]\frac{a_2}{a_1} =\frac{a_3}{a_2}[/tex]
= [tex]\frac{48}{64} =\frac{36}{48}= \frac{3}{4}[/tex]
General explicit formula for G.P. = [tex]a_n= a r^{n-1}[/tex]
Substituting the values :
[tex]a_n= 64 \times (\frac{3}{4})^{n-1}[/tex]
Thus the explicit function represents the geometric sequence of the heights of the toy is [tex]a_n= 64 \times (\frac{3}{4})^{n-1}[/tex]
