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:
By signing up, you agree to our Terms of Service and Privacy Policy
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}).
By signing up, you agree to our Terms of Service and Privacy Policy
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.
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.
- How do you find the indicated term of each arithmetic sequence #a_1=12# d=-7, n=22?
- What single discount is equivalent to successive discounts of 10% and 20%?
- How do you write an nth term rule for #6,-30,150,-750,...# and find #a_6#?
- How do you find the arithmetic means of the sequence -8, __, __, __, __, 7?
- How do you find the sum of the arithmetic sequence having the data given #a_1=7#, d = - 3, n = 20?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7