Question

A 2-column table with 7 rows. Column 1 is labeled Power of 3 with entries 3 cubed, 3 squared, 3 Superscript 1, 3 Superscript 0, 3 Superscript negative 1, 3 Superscript negative 2, 3 Superscript negative 3. Column 2 is labeled Value with entries 27, 9, 3, a, b, StartFraction 1 Over 9 EndFraction, c.

Answer these questions about the powers of 3.


What is the pattern as the exponents decrease?


What is the value of each variable?

a =

b =

c =

Answer 1

Answer:

a=1, b=1/3, c=1/27

Step-by-step explanation:

The table is given below:

$\left|\begin{array}{c|c} Powers of 3&Value\\----&---\\3^3&27\\3^2&9\\3^1&3\\3^0&a\\3^{-1}&b\\3^{-2}&\frac{1}{9} \\3^{-3}&c\end{array}\right|$

(a)As the exponents decrease, the next term is gotten by a division of the previous term by 3.

$f_n=f_{n-1}\div 3$

(b)

$f_n=f_{n-1}\div 3\\I.a=f_n, f_{n-1}=3,\\a=f_n=3\div 3=1\\II. b=f_n, f_{n-1}=1,\\b=f_n=1\div 3=\frac{1}{3}\\III. c=f_n, f_{n-1}=\frac{1}{9},\\c=f_n=\frac{1}{9}\div 3=\frac{1}{27}$

a=1, b=1/3, c=1/27

Answer 2

Answer:

a=1, b=1/3, c=1/27

Step-by-step explanation: