Question

Find an explicit function rule for the following sequence defined over the natural numbers: –7, –1, 9, 23, . . .
A. an=9n²+2
B. an=2n²+9
C. an=9n²-2
D. an=2n²-9

Answer 1

Answer: Choice D

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Reason:

Replace n with 1 in choice A to get

$a_n = 9n^2 + 2\\\\a_1 = 9(1)^2 + 2\\\\a_1 = 11$

Choice A says the first term is 11, but this contradicts the fact that the first term should be -7 instead. Therefore, we cross choice A off the list.

You should find that choice B is the exact same story, so it must be eliminated as well.

Choice C has n = 1 get us $a_1 = 7$ which is close, but we want the result to be negative 7 instead of positive. Choice C is eliminated as well.

The only thing left is choice D. Sure enough, plugging in n = 1 does lead to the first term of -7. If you tried n = 2, then it would get you -1 as the second term, and so on. This confirms choice D is the correct answer.