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

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

Explanation:

Answer 2

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

Explanation:

The table is given below:

`\left|\begin{array}c$Powers of 3&Value\\----&---\\3^3&27\\3^2&9\\3^1&3\\3^0&a\\3^(-1)&b\\3^(-2)&(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)/ 3`

(b)

`f_n=f_(n-1)/ 3\\I.a=f_n, f_(n-1)=3,\\a=f_n=3/ 3=1\\II. b=f_n, f_(n-1)=1,\\b=f_n=1/ 3=(1)/(3)\\III. c=f_n, f_(n-1)=(1)/(9),\\c=f_n=(1)/(9)/ 3=(1)/(27)`

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