All categories

3 years ago

What is the explicit formula for the sequence? -7,-4,-1,2,5

Mathematics

2 answers:

valentinak56 [21]3 years ago

8 0

Answer:

y = -7 + 3(n-1)

Step-by-step explanation:

The basic formula for an explicit formula is:

$a_{n}$ = $a_{1}$ + d(n-1)

The first term is clearly -7 and the common difference is 3 because each term is 3 more than the term before it:

$a_{n}$ = -7 + 3(n-1)

Archy [21]3 years ago

5 0

an =a1+d(n-1)

a1=-7

d= -4--7=-4+7=3

an =-7+3(n-1)

an = -7+ 3n-3

an=-10+3n

You might be interested in

After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is modelled by the function C(t)=8(e

Alexxx [7]

Answer:

the maximum concentration of the antibiotic during the first 12 hours is 1.185 $\mu g/mL$ at t= 2 hours.

Step-by-step explanation:

We are given the following information:

After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is modeled by the function where the time t is measured in hours and C is measured in $\mu g/mL$

$C(t) = 8(e^{(-0.4t)}-e^{(-0.6t)})$

Thus, we are given the time interval [0,12] for t.

We can apply the first derivative test, to know the absolute maximum value because we have a closed interval for t.
The first derivative test focusing on a particular point. If the function switches or changes from increasing to decreasing at the point, then the function will achieve a highest value at that point.

First, we differentiate C(t) with respect to t, to get,

$\frac{d(C(t))}{dt} = 8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)})$

Equating the first derivative to zero, we get,

$\frac{d(C(t))}{dt} = 0\\\\8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)}) = 0$

Solving, we get,

$8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)}) = 0\\\displaystyle\frac{e^{-0.4}}{e^{-0.6}} = \frac{0.6}{0.4}\\\\e^{0.2t} = 1.5\\\\t = \frac{ln(1.5)}{0.2}\\\\t \approx 2$

At t = 0

$C(0) = 8(e^{(0)}-e^{(0)}) = 0$

At t = 2

$C(2) = 8(e^{(-0.8)}-e^{(-1.2)}) = 1.185$

At t = 12

$C(12) = 8(e^{(-4.8)}-e^{(-7.2)}) = 0.059$

Thus, the maximum concentration of the antibiotic during the first 12 hours is 1.185 $\mu g/mL$ at t= 2 hours.

4 0

3 years ago

How much will it cost to borrow $2,500 for a year at a simple interest rate at 14% please explain

Mariana [72]

Principle (P) = $ 2,500

Rate (R) = 14%

Time (T) = 1 year

Simple Interest (SI) = $\frac{PRT}{100}$

SI = $\frac{2500 * 14 * 1}{100} = \frac{25 *14}{1} = 350$

Hence, the answer is $350.

3 0

3 years ago

A ship sails north for 2 hours, traveling a total of 15 miles. Then the ship turns south and travels 6 miles in an hour.

ch4aika [34]

Answer:

3 miles per hour

Step-by-step explanation:

3 0

3 years ago

Plot each complex number and find its absolute value. 2 - 2i

sammy [17]

Answer:

(2,-2) and i think the absolute value might jus be i

8 0

3 years ago

You have been doing research for your statistics class on the prevalence of severe binge drinking among teens. You have decided

Serggg [28]

Answer:

(1.218 ; 1.322)

the confidence interval is appropriate

Step-by-step explanation:

The confidence interval :

Mean ± margin of error

Sample mean = 1.27

Sample standard deviation, s = 0.80

Sample size, n = 914

Since we are using tbe sample standard deviation, we use the T table ;

Margin of Error = Tcritical * s/√n

Tcritical at 95% ; df = 914 - 1 = 913

Tcritical(0.05, 913) = 1.96

Margin of Error = 1.96 * 0.80/√914 = 0.05186

Mean ± margin of error

1.27 ± 0.05186

Lower boundary = 1.27 - 0.05186 = 1.218

Upper boundary = 1.27 + 0.05186 = 1.322

(1.218 ; 1.322)

According to the central limit theorem, sample means will approach a normal distribution as the sample size increases. Hence, the confidence interval is valid, the sample size of 914 gave a critical value at 0.05 which is only marginally different from that will obtained using a normal distribution table. Hence, the confidence interval is appropriate

8 0

3 years ago