An arithmetic sequence is represented by the explicit formula A(n) = 2 +(n − 1)(− 5)

Mathematics

2 answers:

Reil [10]2 years ago

8 0

Answer:

a+(n-1)d please do you get it or

ruslelena [56]2 years ago

8 0

Answer:

$a_{n}$ = $a_{n-1}$ - 5

Step-by-step explanation:

Given the explicit formula

A(n) = 2 - 5(n - 1)

Compare with the standard form

A(n) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = - 5

A recursive formula allows a term in the sequence to be found by adding d to the previous term.

Then recursive formula is

$a_{n}$ = $a_{n-1}$ - 5 , with a₁ = 2

You might be interested in

Find 2x2 − 2z4 + y2 − x2 + z4 if x = −4, y = 3, and z = 2.<br><br> Is -3 the correct answer?

Ket [755]

We're given the algebraic expression 2x^2 - 2z^4 + y^2 - x^2 + z^4

By hypothesis, x = -4, y = 3 and z = 2

Let's replace each letter by its given value:

2x^2 - 2z^4 + y^2 - x^2 + z^4
2(-4)^2 - 2(2)^4 + (3)^2 - (-4)^2 + (2)^4
(2*16) - 2*16 + 9 - 16 + 16
32 - 32 + 9 - 16 + 16
9

So wrong. The correct answer is not -3, but 9.

Hope this helps! :D

6 0

3 years ago

Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee a

rusak2 [61]

Answer:

We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that $\sigma = 2$

If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?

We would need a sample of n.

n is found when $M = 0.5$ . So