Question

Question 19 Find the next two numbers in the pattern. 9,-27,81, -243,.. ​

Answer 1

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:

$(-3)^2; (-3)^3; (-3)^4; (-3)^5;$

Check if it corresponds with the given pattern

$(-3)^2 = 9$        $(-3)^3 = -27$     $(-3)^4 = 81$      $(-3)^5 = -243$

Let the above expression reflect their position in the pattern

$(-3)^{1 + 1}; (-3)^{2 + 1}; (-3)^{3 + 1}; (-3)^{4 + 1};$

By comparing each element;

We have that

$T_n = (-3)^{n+1}$

The next two numbers is when n = 5 and n = 6

When n = 5

$T_5 = (-3)^{5+1}$

$T_5 = (-3)^6$

$T_5 = 729$

When n = 6

$T_6 = (-3)^{6+1}$

$T_6 = (-3)^7$

$T_6 = -2187$

Hence;

729 and -2187 are the next on the list