Question

What is the 23rd term of this pattern: 7, -21, 63, -189,.. and determine if it’s arithmetic or geometric ! Please answer this !!

Answer 1

`a_(23) = 219667417263`

The pattern is geometric.

Step-by-step explanation

The given pattern is:

7, -21, 63, -189,..

We can see from the pattern that,

`r = ( - 189)/(63) = (63)/( - 21) = ( - 21)/(7) = - 3`

Since there is a common ratio of -3, the pattern is geometric.

The first term of this pattern is

`a_1=7`

The nth term of the pattern is given by the formula:

`a_n = a_1 {r}^(n - 1)`

To find the 23rd term, we put, n=23, the first term and the constant ratio.

`a_(23)= 7{ (-3 )}^(23 - 1)`

`a_(23)= 7{ (-3 )}^(22)`

`a_(23) = 219667417263`