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

ANSWER

$a_{23} = 219667417263$

The pattern is geometric.

EXPLANATION

The given pattern is:

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

We can see from the pattern that,

$r = \frac{ - 189}{63} = \frac{63}{ - 21} = \frac{ - 21}{7} = - 3$

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.

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

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

$a_{23} = 219667417263$