Construct a recursive rule to describe the sequence: 2, 4, 6, 8,...

Mathematics

1 answer:

kap26 [50]3 years ago

3 0

Answer:

a[1] = 2; a[n] = a[n-1] + 2

Step-by-step explanation:

The first term of the sequence is 2, so the first part of the definition is ...

a[1] = 2

Each term is 2 more than the previous one, so the rest of the definition is ...

a[n] = a[n-1] + 2

_____

Comment on recursive rules

A recursive rule has two parts. The first part tells what the initial value of the sequence is. The second part relates the next term to the previous term or terms.

For arithmetic and geometric sequences, each term is related to the previous term by a constant. For an arithmetic sequence, each term is the last term plus the common difference. For a geometric sequence, each term is the last term multiplied by the common ratio.

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Nastasia [14]

Answer:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

$z=\frac{0.36 -0.41}{\sqrt{\frac{0.41(1-0.41)}{100}}}=-1.017$

Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

$\hat p=0.36$ estimated proportion with the survey

$p_o=0.41$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.41.:

Null hypothesis: $p\geq 0.41$

Alternative hypothesis: $p < 0.41$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .