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The conjecture of the pattern - 3, 6, - 9, 12 is all the set of series generated by the expression s = (- 1)ⁿ · 3 · n.

What is the conjecture behind a pattern of an arithmetic sequence?

In this problem we have a sequence with a pattern, which has to be translated into mathematical expressions. We notice two features of this sequence:

  1. The elements of the sequence are multiples of 3.
  2. Two consecutive elements have signs opposite to each other.

Then, the pattern can be generated by using the following expression:

s = (- 1)ⁿ · 3 · n

Now we check if the pattern is the same as the shown in the question:

n = 1

s = (- 1)¹ · 3 · 1

s = - 3

n = 2

s = (- 1)² · 3 · 2

s = 6

n = 3

s = (- 1)³ · 3 · 3

s = - 9

n = 4

s = (- 1)⁴ · 3 · 4

s = 12

To learn more on conjectures: https://brainly.com/question/11492642

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