[tex]a_n=72\left(\dfrac{1}{3}\right)^{n-1}\\\\\text{Put}\ n=1,\ n=2,\ n=3,\ n=4,\ n=5\ \text{to the equation}:\\\\n=1\to a_1=72\left(\dfrac{1}{3}\right)^{1-1}=72\left(\dfrac{1}{3}\right)^0=72(1)=72\\\\n=2\to a_2=72\left(\dfrac{1}{3}\right)^{2-1}=72\left(\dfrac{1}{3}\right)^1=72\left(\dfrac{1}{3}\right)=\dfrac{72}{3}=24\\\\n=3\to a_3=72\left(\dfrac{1}{3}\right)^{3-1}=72\left(\dfrac{1}{3}\right)^2=72\left(\dfrac{1}{9}\right)=\dfrac{72}{9}=8\\\\n=4\to a_4=72\left(\dfrac{1}{3}\right)^{4-1}=72\left(\dfrac{1}{3}\right)^3=72\left(\dfrac{1}{27}\right)=\dfrac{72}{27}=\dfrac{8}{3}\\\\n=5\to a_5=72\left(\dfrac{1}{3}\right)^{5-1}=72\left(\dfrac{1}{3}\right)^4=72\left(\dfrac{1}{81}\right)=\dfrac{72}{81}=\dfrac{8}{9}\\\\Answer:\ \boxed{72,\ 24,\ 8,\ \dfrac{8}{3},\ \dfrac{8}{9}}[/tex]
Answer:
The first five terms are as follows:
72, 24, 8, 2.66, 0.88
Step-by-step explanation:
1) Explicit formula:
[tex]72 * 1/3^{n-1}[/tex]
2) Simply replace "n" with 2,3,4 and 5 in order to find the numbers associated with these terms.
a(1) = 72
a(2) = 24
a(3) = 8
a(4) = 2.66
a(5) = 0.88
Note:
In the explicit formula the first term is already provided, so you do not have to find the first term if it has already been given.
