Question

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

Answer 1

729 and -2187 are the next on the list

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