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4 years ago

1, 3, 6, 10, 15 is it arithmetic, geometric or neither

Mathematics

1 answer:

Gekata [30.6K]4 years ago

7 0

The given sequence is neither arithmetic nor geometric.

Further explanation:

In order to check whether a sequence is geometric or arithmetic we have to find the common ratio and common difference respectively

Common difference is the deifference between cunsecutive terms of a sequence while common ratio is the ratio between two consecutive terms.

Common difference is denoted by d and common ratio is denoted by r

If the common difference is same then the given sequence is an arithmetic sequence
If the common ratio is same then the given sequence is a geometric sequence

Given

1, 3, 6, 10, 15

Common difference:

Here

$a_1=1\\a_2=3\\a_3=6\\a_4=10\\a_5=15\\Common\ Difference=a_2-a_1=3-1=2\\a_3-a_2=6-3=3\\a_4-a_3=10-6=4$

As the common difference is not same, the given sequence is not an arithmetic sequence

Common Ratio:

$r=\frac{a_2}{a_1}=\frac{3}{1}=3\\\frac{a_3}{a_2}=\frac{6}{3}=2\\\frac{a_4}{a_3}=\frac{10}{6}=1.6$

As the common ratio is also not same the sequence is not a geometric sequence.

The given sequence is neither arithmetic nor geometric.

Keywords: Arithmetic sequence, Geometric Sequence

Learn more about sequences at:

#LearnwithBrainly

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Alex has a bag of marbles. Each marble is red, blue, or yellow , and the ratio of the red to blue to yellow marbles is 6:10:15.

lesantik [10]

Answer:

There are 150 blue marbles in Alex's bag.

Step-by-step explanation:

Let $x$ , $y$ , $z$ be the quantities of red, blue and yellow marbles, respectively. From statement we derive three rational equations for initial and final ratios:

Initial ratio

$\frac{x}{y} = \frac{6}{10}$ (1)

$\frac{y}{z} = \frac{10}{15}$ (2)

Final ratio

$\frac{x + 10}{z - 25} = \frac{1}{2}$ (3)

After some algebraic handling we get the following system of linear equations:

$x - \frac{3}{5}\cdot y = 0$ (1)

$y - \frac{2}{3}\cdot z = 0$ (2)

$2\cdot (x + 10) = z - 25$

$2\cdot x +20 = z - 25$

$2\cdot x - z = -45$ (3)

The solution of the system of linear equations is:

$x = 90$ , $y = 150$ , $z = 225$

There are 150 blue marbles in Alex's bag.

5 0

3 years ago

A piecewise function g(x) is represented by the graph. Which functions represent a piece of the function? Select three options.

horrorfan [7]

-2 and 2x*56 the other answer is g(x)

6 0

3 years ago

To make cherry turnovers, a cook cuts the dough into triangles with a base of 6 inches and a height of 3 inches. How many turnov

Inessa [10]

Answer:

24 turnovers can be cut from the rectangular piece of dough.

Step-by-step explanation:

Given:

A rectangular piece of dough is 12 inches wide and 18 inches long.

To make cherry turnovers, a cook cuts the dough into triangles with a base of 6 inches and a height of 3 inches.

Now, to find the number of turnovers can be cut from the dough.

So, we find the area of the triangle the cook cuts from the dough by putting formula:

Base (b) = 6 inches.

Height (h) = 3 inches.

$Area=\frac{hb}{2} \\\\Area=\frac{h\times b}{2} \\\\Area=\frac{3\times 6}{2} \\\\Area=\frac{18}{2} \\\\Area=9\ inches^2.$

Thus, the area of the triangle cut from the dough is 9 inches².

Now, to get the area of rectangular piece of dough by putting formula:

Length = 18 inches.

Width = 12 inches.

$Area=length\times width\\\\Area=18\times 12\\\\Area=216\ inches^2.$

Hence, the area of the rectangular dough is 216 inches².

Now, to get the number of turnovers can be cut from the rectangular piece of dough we divide the area of the rectangular dough by the area of the triangle cut from the dough:

$\frac{216}{9} \\\\=24\ turnovers.$

Therefore, 24 turnovers can be cut from the rectangular piece of dough.

8 0

4 years ago

HOW DO I FIND QR PLEASE HELP

Paul [167]

Solution: For finding QR we need to apply Pythagoras Theorem

What is Pythagoras Theorem ?

ans : Pythagoras Theorem is the sum of square of two sides which is equal to the third side or the hypotenuse. This formula is valid oy incase of Right-Angled Traingle because one of three angles here is 90°

According to this law let's apply it in the diagram shown here.

(Hypotenuse)² = (Adjacent)² + (Opposite)²

(PR)² = (QR)² + (PQ)²

(5x - 2)² = (QR)² + (3x - 1)²

(QR)² = (5x - 2)² - (3x - 1)²

After factorising both of them we get

(QR)² = 25x² - 20x + 4 - (9x² - 6x + 1)

(QR)² = 25x² - 20x + 4 - 9x² + 6x - 1

(QR)² = 16x² - 14x + 3

QR = √(16x² - 14x + 3)

So, QR is √(16x² - 14x + 3)

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3 years ago

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4 years ago