All categories

2 years ago

What are the explicit equation and domain for a geometric sequence with a first term of 3 and a second term of −9?

2 answers:

8 0

U can find the common ratio by dividing the 2nd term by the first term
r = -9/3 = -3

an = a1 * r^(n - 1)
a1 = 1st term = 3
r = common difference = -3
now sub
an = 3 * -3^(n - 1) <== ur formula
domain : all integers where n > = 1 <==

ella [17]2 years ago

6 0

Answer: $\ a_{n}=3(-3)^{n-1}$

Step-by-step explanation:

Given: A geometric sequence with its first term $a_1=a=3$

and second term $a_2=-9$

We know that the common ratio in of a geometric sequence= $\frac{a_{n}}{a_{n-1}}$

Thus, common ratio $r=\frac{-9}{3}=-3$

We know that the explicit rule for geometric sequence is written as

$a_{n}=ar^{n-1}\\\Rightarrow\ a_{n}=3(-3)^{n-1}..[\text{by substituting the values of 'a' and 'r' in it }]$

Thus, the explicit rule for the given geometric sequence is $\ a_{n}=3(-3)^{n-1}$ for every n ,a natural number.

You might be interested in

One way to measure whether the trees in the Wade Tract are uniformly distributed is to examine the average location in the north

tatyana61 [14]

Answer:

Null hypothesis be H₀ : μ = 100

Alternative hypothesis Hₐ : μ < 100

There is sufficient statistical evidence to suggest that the average location of Wade Tract is 100

Step-by-step explanation:

Here we have;

Let our null hypothesis be H₀ : μ = 100 Average location of trees in the Wade Tract is 100

Our alternative hypothesis becomes Hₐ : μ < 100 at 95% confidence level

Proposed average location in Wade Tract, μ = 100

Sample mean, $\bar x$ = 99.74

Standard deviation, s = 58

Sample size, n = 584

The t test formula is therefore;

$t=\frac{\bar{x}-\mu }{\frac{s }{\sqrt{n}}}$

Therefore, with df = 584 -1 = 583, and α = (1 - 0.95)/2 = 0.025

We have $t_{\alpha /2}$ = -1.65

Plugging in the values into the t test formula, we have t = -0.108338, from which the p-value is given as p = 0.4569 which is much more than the value of α, therefore, we accept the null hypothesis as follows;

There is sufficient statistical evidence to suggest that the average location of Wade Tract = 100.

7 0

2 years ago

Discuss the validity of the following statement. If the statement is always true, explain why. If not, give a counterexample.

Zarrin [17]

Correction:

Because F is not present in the statement, instead of working onP(E)P(F) = P(E∩F), I worked on

P(E∩E') = P(E)P(E').

Answer:

The case is not always true.

Step-by-step explanation:

Given that the odds for E equals the odds against E', then it is correct to say that the E and E' do not intersect.

And for any two mutually exclusive events, E and E',

P(E∩E') = 0

Suppose P(E) is not equal to zero, and P(E') is not equal to zero, then

P(E)P(E') cannot be equal to zero.

P(E)P(E') ≠ 0

This makes P(E∩E') different from P(E)P(E')

Therefore,

P(E∩E') ≠ P(E)P(E') in this case.

8 0

2 years ago

A bowl of flower seeds contains 5 petunia seeds and 15 begonia seeds. Riley calculated the probability that a random selected se

Vlad1618 [11]

Answer:

Riley divided the number of petunia seeds by the number of begonia seeds, getting $\frac {5}{15} = \frac {1}{3}$ . What you actually need to do to calculate the probability of selecting a petunia seed is divide the number of petunia seeds by the <em>total</em> number of seeds. 5 petunia seeds and 15 begonia seeds makes 20 total seeds, so you divide 5 petunia seeds by 20 total seeds to get $\frac {5}{20} = \frac {1}{4}$ .

7 0

2 years ago

The infield of a baseball field is a square

AnnZ [28]

Answer:

106.1 ft/s

Step-by-step explanation:

You know the diagonal of a square is √2 times the length of one side, so the distance from 3rd to 1st is 90√2 feet ≈ 127.2792 ft.

The speed is the ratio of distance to time:

speed = distance/time = 127.2972 ft/(1.2 s) ≈ 106.1 ft/s.

_____

In case you have never figured or seen the computation of the diagonal of a square (the hypotenuse of an isosceles right triangle), consider the square with side lengths 1. The diagonal will cut the square into halves that are isosceles right triangles with leg lengths 1. Then the Pythagorean theorem can be used to find the diagonal length d:

d² = 1² + 1²

d² = 2

d = √2

Since this is the diagonal for a side length of 1, any other side length will serve as a scale factor for this value. A square with a side length of 90 ft will have a diagonal measuring 90√2 ft.

7 0

2 years ago

In two sample surveys, 125 people were asked about their favorite fruit. In the first survey, 40 people chose apples, 64 chose o

Artemon [7]

Answer: Marianne made an inference that is true based on the data. More than half of the people surveyed in each sample chose oranges as their favorite fruit. Since most people in each sample chose oranges, it is likley that oranges are the favorite fruit of the entire population.

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers