# How do you find the nth term of the sequence #1/2, 1/4, 1/8, 1/16, ...#?

By signing up, you agree to our Terms of Service and Privacy Policy

The nth term of the sequence (1/2, 1/4, 1/8, 1/16, \ldots) can be found using the formula for a geometric sequence:

[a_n = a_1 \cdot r^{(n-1)}]

where:

- (a_n) is the nth term of the sequence,
- (a_1) is the first term of the sequence,
- (r) is the common ratio, which is the number each term is multiplied by to get the next term, and
- (n) is the term number.

In this sequence, the first term (a_1) is (1/2), and the common ratio (r) is (1/2) because each term is half of the previous one.

Plugging these values into the formula, we get:

[a_n = \frac{1}{2} \cdot \left(\frac{1}{2}\right)^{(n-1)}]

Simplifying this expression gives us the nth term of the sequence:

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

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.

- What is a collapsing infinite series?
- Is the series #\sum_(n=0)^\infty1/((2n+1)!)# absolutely convergent, conditionally convergent or divergent?
- How do you determine if the summation #n^n/(3^(1+2n))# from 1 to infinity is convergent or divergent?
- Using the definition of convergence, how do you prove that the sequence #lim 1/(6n^2+1)=0# converges?
- How do you apply the ratio test to determine if #sum_(n=1)^oo 3^n# is convergent to divergent?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7