Answer:
729 and -2187 are the next on the list
Step-by-step explanation:
Given
9,-27,81, -243,..
Required
Determine the next two numbers
The first step is to determine the formula that guides the pattern
Start by expressing all elements in the pattern as a base of -3
This gives:
[tex](-3)^2; (-3)^3; (-3)^4; (-3)^5;[/tex]
Check if it corresponds with the given pattern
[tex](-3)^2 = 9[/tex] [tex](-3)^3 = -27[/tex] [tex](-3)^4 = 81[/tex] [tex](-3)^5 = -243[/tex]
Let the above expression reflect their position in the pattern
[tex](-3)^{1 + 1}; (-3)^{2 + 1}; (-3)^{3 + 1}; (-3)^{4 + 1};[/tex]
By comparing each element;
We have that
[tex]T_n = (-3)^{n+1}[/tex]
The next two numbers is when n = 5 and n = 6
When n = 5
[tex]T_5 = (-3)^{5+1}[/tex]
[tex]T_5 = (-3)^6[/tex]
[tex]T_5 = 729[/tex]
When n = 6
[tex]T_6 = (-3)^{6+1}[/tex]
[tex]T_6 = (-3)^7[/tex]
[tex]T_6 = -2187[/tex]
Hence;
729 and -2187 are the next on the list
