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3 years ago

Identify the recursive formula for the following sequence: 8, 26, 80, 242, . . .

Mathematics

2 answers:

AVprozaik [17]3 years ago

7 0

Answer:

Recursive formula is $a_n = (a_{n-1} *3) + 2$

Step-by-step explanation:

8, 26, 80, 242, . . .

8 is the first term

To get 26 we multiply 8 by 3 and then add 2

8*3 = 24 + 2= 26

26 * 3= 78+2 = 80

80*3 = 240 + 2 = 242

So to get next term we multiply the previous term by 3 and then we add 2

$a_n = (a_{n-1} *3) + 2$

prisoha [69]3 years ago

6 0

Answer:

an = 3an – 1 + 2 where a1 = 8

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about 7.5 gallons of water fill up 1 cubic foot of space. how many gallons of water will fill a goldfish pool shaped like the pr

Murrr4er [49]

The volume of the goldfish pool is V= 0.5ft x 1.5ft x 3ft=2.25 ft^3
so 7.5gallons ----------> 1 ft^3
x=? <----------- 2.25 ft^3
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the answer is 16.87 gallons of water

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4 years ago

To graph ( 0, 15 ) what is the only direction you will move

Dominik [7]

Answer:

you will only move 15 units up

Step-by-step explanation:

since the y is the only one that has a value, then you will have to focus more on the direction where the y will go. and since the y's value is positive then you will have to go upwards.

3 0

3 years ago

Can a math god help me out?

Taya2010 [7]

Answer:

$f(1)=70$

$f(n)=f(n-1)+6$

Step-by-step explanation:

One is given the following function:

$f(n)=64+6n$

One is asked to evaluate the function for $(f(1))$ , substitute $(1)$ in place of $(n)$ , and simplify to evaluate:

$f(1)=64+6(1)$

$f(1)=64+6$

$f(1)=70$

A recursive formula is another method used to represent the formula of a sequence such that each term is expressed as a function of the last term in the sequence. In this case, one is asked to find the recursive formula of an arithmetic sequence: that is, a sequence of numbers where the difference between any two consecutive terms is constant. The following general formula is used to represent the recursive formula of an arithmetic sequence:

$a_n=a_(_n_-_1_)+d$

Where ( $a_n$ ) is the evaluator term ( $a_(_n_-_1_)$ ) represents the term before the evaluator term, and (d) represents the common difference (the result attained from subtracting two consecutive terms). In this case (and in the case for most arithmetic sequences), the common difference can be found in the standard formula of the function. It is the coefficient of the variable (n) or the input variable. Substitute this into the recursive formula, then rewrite the recursive formula such that it suits the needs of the given problem,

$a_n=a_(_n_-_1_)+d$

$a_n=a_(_n_-_1_)+6$

$f(n)=f(n-1)+6$

3 0

3 years ago

If f(x)=4x^2+1 and g(x) =x^2-5 find (f-g)(x)

docker41 [41]

Answer:

$\huge\boxed{(f-g)(x)=3x^2+6}$

Step-by-step explanation:

$(f-g)(x)=f(x)(x)\\\\\text{substitute}\ f(x)=4x^2+1\ \text{and}\ g(x)=x^2-5\\\\(f-g)(x)=(4x^2+1)-(x^2-5)=4x^2+1-x^2-(-5)=4x^2+1-x^2+5\\\\\text{combine like terms}\\\\(f-g)(x)=(4x^2-x^2)+(1+5)=3x^2+6$

6 0

4 years ago

Location is known to affect the number, of a particular item, sold by an auto parts facility. Two different locations, A and B,

Mama L [17]

We have two samples, A and B, so we need to construct a 2 Samp T Int using this formula:

$\displaystyle \overline {x}_1 - \overline {x}_2 \ \pm \ t^{*} \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} }$

In order to use t*, we need to check conditions for using a t-distribution first.

Random for both samples -- NOT STATED in the problem ∴ proceed with caution!
Independence for both samples: 130 < all items sold at Location A; 180 < all items sold at Location B -- we can reasonably assume this is true
Normality: CLT is not met; n < 30 for both locations A and B ∴ proceed with caution!

Since 2/3 conditions aren't met, we can still proceed with the problem but keep in mind that the results will not be as accurate until more data is collected or more information is given in the problem.

Solve for t*:

We need the tail area first.

$\displaystyle \frac{1-.9}{2}= .05$

Next we need the degree of freedom.

The degree of freedom can be found by subtracting the degree of freedom for A and B.

The general formula is df = n - 1.

df for A: 13 - 1 = 12
df for B: 18 - 1 = 17
df for A - B: |12 - 17| = 5

Use a calculator or a t-table to find the corresponding t-score for df = 5 and tail area = .05.

t* = -2.015

Now we can use the formula at the very top to construct a confidence interval for two sample means.

$\overline {x}_A=39$
$s_A=8$
$n_A=13$
$\overline {x}_B = 55$
$s_B=2$
$n_B=18$
$t^{*}=-2.015$

Substitute the variables into the formula: $\displaystyle \overline {x}_1 - \overline {x}_2 \ \pm \ t^{*} \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} }$ .

$39-55 \ \pm \ -2.015 \big{(}\sqrt{\frac{(8)^2}{13} +\frac{(2)^2}{18} } } \ \big{)}$

Simplify this expression.

$-16 \ \pm \ -2.015 (\sqrt{5.1453} \ )$
$-16 \ \pm \ 3.73139$

Adding and subtracting 3.73139 to and from -16 gives us a confidence interval of:

$(-20.5707,-11.4293)$

If we want to interpret the confidence interval of (-20.5707, -11.4293), we can say...

We are 90% confident that the interval from -20.5707 to -11.4293 holds the true mean of items sold at locations A and B.

5 0

2 years ago