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4 years ago

Which of the following functions generates the sequence 0, 2, 4, 6, ...?

Mathematics

1 answer:

boyakko [2]4 years ago

5 0

Answer:

F(n) = 2n – 2

Step-by-step explanation:

The sequence 0, 2, 4, 6

First, let us determine if the sequence is arithmetic progression (A.P) or geometric progression (G.P)

This is illustrated:

Let us calculate the common difference (d)

Common difference (d) = 2nd term – first term

Common difference (d) = 3rd term – 2nd term

=> 2 – 0 = 2

=> 4 – 2 = 2

The common difference (d) = 2.

Common ratio (r) = 2nd term /1st term

Common ratio (r) = 3rd term /2nd term

=> 2/0 = undefined

=> 4/2 = 2

There is no common ratio.

Since we have a common difference, therefore the sequence is arithmetic progression.

Now, let us obtain an expression for the sequence.

This can be obtained by using the arithmetic progression formula as shown below:

F(n) = a + (n – 1)d

a is the first term

n is the number of term

d is the common difference.

The sequence 0, 2, 4, 6

The first term (a) = 0

Common difference (d) = 2

F(n) = a + (n – 1)d

F(n) = 0 + (n – 1)2

F(n) = 2n – 2

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Ben is 12 years older than Ishaan. Ben and Ishaan first met two years ago. Three years ago, Ben was 4 times as old as Ishaan.

bixtya [17]

So, the 2 equations would be.... B -12 = I and (B - 3) = 4(I - 3) the second sentence is irrelevant.
B - 3 = 4 (I) - 12
B - 3 = 4B - 48 - 12
B - 4B = -60 + 3
-3B = -57
B (Ben) = 19
Ishaan is 7

Hope this helps!

5 0

3 years ago

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40 is 160% of what number?<br>

san4es73 [151]

Answer:

Step-by-step explanation:

3 0

3 years ago

Grades in large classes are sometimes approximately Normally distributed—a fact that serves as the justification for "grading on

QveST [7]

Answer:

Grade A: $Z \geq 1$

Grade B: $0 \leq Z < 1$

Grade C: $-1 \leq Z < 0$

Grade D: $Z < -1$

Step-by-step explanation:

Problems of normally distributed samples can be solved using the Z score table.

The Z score of a measure represents how many standard deviations it is above or below the mean of all the measures.

Each Z score has a pvalue. This represents the percentile of the measure.

In this problem, we have that:

The upper 16% of the class get A grades. The upper 16% has a pvalue of at least 100% = 16% = 84% = 0.84. This is $Z \geq 1$ .

The middle 34% of the class get B grades. The middle 34% has a pvalue of at least 84%-35% = 50% = 0.5 and at most 0.84. This is $0\leqZ < 1$ .

Those between a pvalue of 0.5-0.34 = 0.16 and 0.5 get get grade C. $Z = -1$ has a pvalue of 0.16. So a grade C is in the interval $-1 \leq Z < 0$ .

Those with Z lesser than -1 get grades D and F

6 0

3 years ago

Solve −3x2 + 30x − 90 = 0

Ray Of Light [21]

Step-by-step explanation:

so, it is a quadratic equation :

-3x² + 30x - 90 = 0

the first thing we can do is divide by 3

-x² + 10x - 30 = 0

remember, the formula to solve and find the 2 solutions is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case here

a = -1

b = 10

c = -30

x = (-10 ± sqrt(100 - 4×-1×-30))/-2 =

= (-10 ± sqrt(100 - 120))/-2 = (-10 ± sqrt(-20))/-2 =

= (-10 ± sqrt(4×5)i)/-2 = (-10 ± 2×sqrt(5)i)/-2 =

= 5 ± -sqrt(5)i

x1 = 5 - sqrt(5)i

x2 = 5 + sqrt(5)i

remember, i = sqrt(-1), a complex number.

6 0

3 years ago

What is the 6th term of the geometric sequence where a1 = 1,024 and a4 = −16? 1 −0.25 −1 0.25

VLD [36.1K]

The n-th term is given by

$a_n=a_1\cdot r^{(n-1)}\qquad\text{where r is the common ratio}$

Then we can find the common ratio from the given terms.

$\dfrac{a_4}{a_1}=\dfrac{a_1\cdot r^{(4-1)}}{a_1}=r^3=\dfrac{-16}{1024}=\left(\dfrac{-1}{4}\right)^3\\\\r=\dfrac{-1}{4}\\\\a_6=1024\left(\dfrac{-1}{4}\right)^5=-1$

The appropriate choice is -1.

8 0

4 years ago

Read 2 more answers