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

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ANSWER


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

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