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3 years ago

What is the common difference in the following arithmetic sequence? 2/3, 1/6, -1/3,-5/6....

Mathematics

2 answers:

Komok [63]3 years ago

8 0

Answer:

Common difference $=\frac{-1}{2}$

Step-by-step explanation:

We have general form of arithmetic sequence

a, a+d, a+2d, a+3d ...................

Here it is given that the sequence is

2/3, 1/6, -1/3,-5/6....

Comparing we will get

$a=\frac{2}{3}$

$a+d=\frac{1}{6}\\\\\frac{2}{3}+d=\frac{1}{6}\\\\d=\frac{1}{6}-\frac{2}{3}=\frac{-3}{6}=\frac{-1}{2}$

So common difference $=\frac{-1}{2}$

ratelena [41]3 years ago

5 0

-1/2 is the answer on edgenuty

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The ratio of the numerator to the denominator of a fraction is 2 to 3. If both the numerator and the denominator are increased b

masha68 [24]

Answer:

The fraction is $\frac{4}{6}$

Option (B) is correct.

$3n-2d=0$ and $4n+8=3d+6$

Step-by-step explanation:

Let n denotes numerator and d denotes denominator of the fraction.

Given : The ratio of the numerator to the denominator of a fraction is 2 to 3.

That is $\frac{n}{d}=\frac{2}{3}$

Cross multiply , we get,

$3n=2d$

Or, $3n-2d=0$ ........(1)

Also, given : . If both the numerator and the denominator are increased by 2, the fraction becomes 3/4

That is $\frac{n+2}{d+2}=\frac{3}{4}$

Cross multiply , We get,

$4{n+2}={3}{d+2}$

$4n+8=3d+6$ .........(2)

$3d-4n=2$ .......(3)

Thus, from (1) and (2) , option (B) follows.

Solving equation (1) and (3) to get the original fraction using elimination method,

3n - 2d = 0 ............(1)

and 3d - 4n = 2 .........(3)

Multiply equation (1) by 3 , we get ,

9n - 6d = 0 ..........(4)

Multiply equation (3) by 2 , we get ,

-8n + 6d = 4 ..........(5)

Adding (4) and (5) , we get,

9n - 6d -8n + 6d = 4 + 0

⇒ n = 4

Put n = 4 in (1), we get

3n - 2d = 0 ⇒ 3(4) - 2d = 0 ⇒ 12 -2d = 0 ⇒ 12 = 2d ⇒ d = 6

so, the numerator is 4 and the denominator is 6.

Thus, the fraction is $\frac{4}{6}$

6 0

3 years ago

Can someone plz help me

Illusion [34]

First rectangle:
Has 3 cubes in each 5 layers, and imagine it, so we have all dimension needed which is:
l=3 unit
w=1 unit
h=5 unit.
V=l×w×h
V=3×1×5
V=15 cubic inches.

Second rectangular:
Doing the same like that to get:
l=5 unit
w=1 unit
h=3 unit
V=15 cubic inches. As a result, there are no prism that are greater to each other, which mean that they have the same volume of 15 cubic inches. Hope it help!

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3 years ago

What is the exact volume of a cylinder that has a radius of 9.2 in. and a height of 3.7 in.?

charle [14.2K]

$The\ volume\ of\ a\ cylinder:V=\pi r^2\cdot H\\/r-a\ radius;\ H-a\ height/\\--------------------\\r=9.2\ in;\ H=3.7\ in\\\\subtitute\\\\V=\pi\cdot9.2^2\cdot3.7=84.64\cdot3.4\pi=\boxed{287.776\pi\ (in^3)}\approx\boxed{903.62\ (in^3)}\\\\Used\ \pi\approx3.14$
and
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up (+1).

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4 years ago

Write a multiplication equation using one whole number and one fraction that will have a product of 18/8

bezimeni [28]

You could use the solution of 9/4 times 2

8 0

4 years ago

What is the nth term rule of the linear sequence below?<br> 5,8,11,14,17.<br> Tn=

Art [367]

Answer:

Tn = 5 +3(n -1)

Step-by-step explanation:

The first term of the sequence is a1 = 5. The common difference of the terms of the sequence is d = 8-5 = 3. The general term is ...

Tn = a1 +d(n -1)

Tn = 5 +3(n -1) . . . . . . fill in the values for this sequence.

_____

<em>Additional comment</em>

If you like, you can simplify this to ...

Tn = 3n +2

To read more about sequence formulas, see ...

brainly.com/question/26861523

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3 years ago