# How do you write an nth term rule for #a_1=-1/2# and #a_4=-16#?

I'm going to assume that since this is under the Geometric Sequences category, you're looking for a geometric sequence.

A geometric sequence's general term can be found using the following formula:

In our instance, we discover:

Thus, the only practical fix is:

or, if you'd rather:

Additionally, there are two complex solutions, which match up with:

and:

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To write an nth term rule for the sequence given (a_1 = -\frac{1}{2}) and (a_4 = -16), we can first find the common ratio ((r)) by dividing any term by its preceding term. Then, we can use the formula for the nth term of a geometric sequence, which is (a_n = a_1 \times r^{n-1}), where (a_n) represents the nth term of the sequence.

Given (a_1 = -\frac{1}{2}) and (a_4 = -16), we can find the common ratio ((r)) by dividing (a_4) by (a_1).

[ r = \frac{a_4}{a_1} = \frac{-16}{-\frac{1}{2}} = 32 ]

Now that we have the common ratio ((r = 32)), we can use the formula for the nth term of a geometric sequence:

[ a_n = a_1 \times r^{n-1} ]

Substituting the values (a_1 = -\frac{1}{2}) and (r = 32) into the formula, we get:

[ a_n = -\frac{1}{2} \times 32^{n-1} ]

Therefore, the nth term rule for the given sequence is (a_n = -\frac{1}{2} \times 32^{n-1}).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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