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3 years ago

Based on the pattern what are the next two terms for the pattern 4,12,20,28

Mathematics

1 answer:

alukav5142 [94]3 years ago

8 0

Answer:

your next two numbers are 36 and 44

Step-by-step explanation:

because you are adding on 8 to each number

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What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

5 0

3 years ago

The Falcone family is planning to drive from Syracuse, New York to Buffalo, New York. On a map with a scale of

Ad libitum [116K]

Answer:

The Falcones have to travel at 25 m/h to make the trip in 2 hours.

Step-by-step explanation:

In order to find the answer you have to use the formula to calculate speed:

speed=distance/time

distance=50 miles. The stament indicates that the distance between Syracuse and Buffalo is 1 inch and that the map has a scale of inch = 50 miles.

time=2 hours

Now, you can replace the values on the formula:

speed=50 miles/2 hours

speed=25 m/h

According to this, the answer is that the Falcones have to travel at 25 m/h to make the trip in 2 hours.

7 0

3 years ago

The sides of a triangle are 1, x, and x2. what are possible values of x?

Whitepunk [10]

The sides of the triangle are given as 1, x, and x².

The principle of triangle inequality requires that the sum of the lengths of any two sides should be equal to, or greater than the third side.

Consider 3 cases
Case (a): x < 1,
Then in decreasing size, the lengths are 1, x, and x².
We require that x² + x ≥ 1
Solve x² + x - 1 =
x = 0.5[-1 +/- √(1+4)] = 0.618 or -1.618.
Reject the negative length.
Therefore, the lengths are 0.382, 0.618 and 1.

Case (b): x = 1
This creates an equilateral triangle with equal sides
The sides are 1, 1 and 1.

Case (c): x>1
In increasing order, the lengths are 1, x, and x².
We require that x + 1 ≥ x²
Solve x² - x - 1 = 0
x = 0.5[1 +/- √(1+4)] = 1.6118 or -0.618
Reject the negative answr.
The lengths are 1, 1.618 and 2.618.

Answer:
The possible lengths of the sides are
(a) 0.382, 0.618 and 1
(b) 1, 1 and 1.
(c) 2.618, 1.618 and 1.

7 0

4 years ago

Determine the answer to 3 + (-5) and explain the steps using a number line

Andreas93 [3]

Answer:

-2

Step-by-step explanation:

3 - 5 = -2

Place the dot on -2 on the number line that is on your problem as the answer. To show the steps on the number line, use your jumps to go back. For example, your starting point will be on 3, and then use your jumps to go back by 5; that means you go into the negatives. For this case, it is -2.

4 0

3 years ago

Solve the simultaneous equation x^2-4y^2=9 and x+2y=1

Salsk061 [2.6K]

Answer:

x=5,y=-2

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers