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3 years ago

Write a recursive formula for the arithmetic sequence below. What is the value of the 8th term?

Mathematics

2 answers:

Rufina [12.5K]3 years ago

7 0

Answer:

Value of the 8th term = 29

Step-by-step explanation:

We have to write a recursive formula for the arithmetic sequence given as 1, 5, 9, 13......

For an arithmetic sequence recursive formula is

$T_{n}=1+(n-1)4$

= 1 + 4n - 4

$T_{n}=4n-3$

Now 8th term will be $T_{8}$ = ( 4 × 8 - 3 )

= 32 - 3

= 29

Value of the 8th term = 29

Bumek [7]3 years ago

4 0

To find the answer,

Multiply the term with 4 then subtract with 3

Lets take the term as 'n'

Formula = 4n-3

Value of 8th term = (4*8)-3
= 32-3
= 29

The value of 8th term is 29

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3 years ago

-8<2x-4<4 solve the inequality

il63 [147K]

Answer:

Step-by-step explanation:

The inequality will be split into two

It is know that, if a<b<c

Then a<b and b<c

-8<2x-4<4

Apply that to this

Then,

-8<2x-4. Equation 1

Also,

2x-4<4 equation 2

Solving equation 1

-8<2x-4

Add 4 to both side of the equation

-8+4<2x-4+4

-4<2x

Divide both sides by 2

-4/2<2x/2

-2<x

Note, if a is less than b, then, b is greater than a, e.g. 4 is less than 10, this implies 10 is greater than 4

Therefore,

-2<x

Then, x greater than -2

Equation 2

2x-4<4

Add 4 to both side of the inequalities

2x-4+4<4+4

2x<8

Divide both side by 2

Then,

2x/2<8/2

x<4

Therefore x is between -2 and +4.

Check attachment for graphical solution

7 0

3 years ago

Indica el valor del 3 en cada uno de los siguientes números 35.097 _ 753.978 _ 7.543 _ 312.501

lara31 [8.8K]

Free points pls and thank you

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3 years ago

Zander read 13 3/4pages in 1/4 of an hour. Sydney read 43 1/3 pages in 2/3 of an hour. At these rates, would Zander or Sydney re

kakasveta [241]

Answer:

At these rates Sydney read 10 pages per hour more than Zander.

Step-by-step explanation:

Zander read $13\frac{3}{4}$ pages in $\frac{1}{4}$ of an hour.

Therefore, pages read by Zander in 1 hour = $\frac{\text{Total pages read}}{\text{Total time taken}}$

= $\frac{13\frac{3}{4}}{\frac{1}{4}}$

= $\frac{55}{4}\times \frac{4}{1}$

= 55 pages per hour

Sydney read $43\frac{1}{3}$ pages in $\frac{2}{3}$ of an hours.

Pages read by Sydney in 1 hour = $\frac{43\frac{1}{3}}{\frac{2}{3} }$

= $\frac{130}{3}\times \frac{3}{2}$

= 65 pages per hour

Therefore, number of pages read more by Sydney as compared to Zander,

= 65 - 55

= 10 pages per hour

At these rates Sydney read 10 pages per hour more than Zander.

4 0

3 years ago

A random sample of 100 observations from a quantitative population produced a sample mean of 22.8 and a sample standard deviatio

natima [27]

Answer:

We conclude that the population mean is 24.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 24

Sample mean, $\bar{x}$ = 22.8

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, s = 8.3

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 24\\H_A: \mu \neq 24$

We use Two-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{22.8 - 24}{\frac{8.3}{\sqrt{100}} } = -1.44$

We calculate the p-value with the help of standard z table.

P-value = 0.1498

Since the p-value is greater than the significance level, we accept the null hypothesis. The population mean is 24.

Now, $z_{critical} \text{ at 0.05 level of significance } = \pm 1.96$

Since, the z-statistic lies in the acceptance region which is from -1.96 to +1.96, we accept the null hypothesis and conclude that the population mean is 24.

7 0

3 years ago