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what is 30th term of -12, -3, 6, 15

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Step-by-step explanation:

We can see that the difference of every term in the given sequence is 9, because -12 + 9 = -3, -3 + 9 = 6 and 6 + 9 = 15. We may therefore assume that the sequence is arithmetic (a fancy word of saying that a sequence is increasing with a constant value every term).

Since the difference of every term is 9, we know that the explicit form of the sequence (where the value of every term is expressed in terms of the term number) is in the form , where is the term number and is a constant we are going to figure out right now.

We know that the first term of the sequence is -12, so we see that and hence . Therefore, the 30th term of the sequence is .