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3 years ago

What is the recursive formula for the geometric sequence with this explicit formula? an=6*(-1/4)^(n-1)

Mathematics

1 answer:

igomit [66]3 years ago

5 0

Answer:

Step-by-step explanation:

The explicit formula for a geometric sequence is

$a_{n}$ = a₁ $(r)^{n-1}$

where a₁ is the first term and r the common ratio

Given the explicit formula

$a_{n}$ = 6 $(-\frac{1}{4}) ^{n-1}$

where a₁ = 6 and r = - $\frac{1}{4}$

A recursive formula allows any term in the sequence to be found by multiplying the previous term by r , thus

$a_{n}$ = $a_{n-1}$ (- $\frac{1}{4})$ with a₁ = 6 → A

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natita [175]

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3 years ago

HELP! o.o

goblinko [34]

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4 years ago

Read 2 more answers

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 3639 3639 miles, with a var

Andrei [34K]

Answer:

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

A reminder is that the standard deviation is the square root of the variance.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .