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3 years ago

The common difference of the arithmetic sequence

Mathematics

2 answers:

oksian1 [2.3K]3 years ago

5 0

Answer:

its 1/3

Step-by-step explanation:

please mark it as brainliest!!<3

Ilya [14]3 years ago

4 0

Answer:

We conclude that the common difference of the Arithmetic sequence is: 1/3

Step-by-step explanation:

Given the Arithmetic sequence

1/2, 5/6, 7/6, 3/2, 11/6

We know that an Arithmetic sequence has a constant common difference.

Let us compute the common difference 'd' of all the adjacent terms

$\frac{5}{6}-\frac{1}{2}=\frac{1}{3},\:\quad \frac{7}{6}-\frac{5}{6}=\frac{1}{3},\:\quad \frac{3}{2}-\frac{7}{6}=\frac{1}{3},\:\quad \frac{11}{6}-\frac{3}{2}=\frac{1}{3}$

The difference between all the adjacent terms is the same and equal

Therefore,

$d=\frac{1}{3}$

Hence, we conclude that the common difference of the Arithmetic sequence is: 1/3

You might be interested in

What should be subtracted from -8767 to obtain 7676

MissTica

Answer:

16443

Step-by-step explanation:

a = 7676 - b

b = -8767

then:

a = 7676 - (-8767)

a = 7676 + 8767

a = 16443

Check:

16443 -8767 = 7676

5 0

3 years ago

What is the distance of BC?

Aliun [14]

Answer:

BC = 9 miles

Step-by-step explanation:

Here, we are given ΔABC ∼ ΔEDC, which means both triangles are similar and they tend to have the same dimensions and properties.

To find the length of BC, we are given the proportion:

$\frac{12}{8} = \frac{x}{6}$

Where x represents the length BC.

Solving further, let's cross multiply

$12 * 6 = 8x$

$72 = 8x$

Solving for x, we have:

$8x = 72$

Lets divide both sides by 8

$\frac{8x}{8} = \frac{72}{8}$

$x = 9$

Therefore the distance BC is 9 miles

5 0

3 years ago

PLS HELP ASAP!!! I’ll give brainliest

iren [92.7K]

The answer is at least 11 weeks not almost.

5 0

3 years ago

If X²⁰¹³ + 1/X²⁰¹³ = 2, then find the value of X²⁰²² + 1/X²⁰²² = ?

enyata [817]

Step-by-step explanation:

$\bf➤ \underline{Given-} \\$

$\sf{x^{2013} + \frac{1}{x^{2013}} = 2}\\$

$\bf➤ \underline{To\: find-} \\$

$\sf {the\: value \: of \: x^{2022} + \frac{1}{x^{2022}}= ?}\\$

$\bf ➤\underline{Solution-} \\$

Let us assume that:

$\rm: \longmapsto u = {x}^{2013}$

Therefore, the equation becomes:

$\rm: \longmapsto u + \dfrac{1}{u} = 2$

$\rm: \longmapsto \dfrac{ {u}^{2} + 1}{u} = 2$

$\rm: \longmapsto{u}^{2} + 1 = 2u$

$\rm: \longmapsto{u}^{2} - 2u + 1 =0$

$\rm: \longmapsto {(u - 1)}^{2} =0$

$\rm: \longmapsto u = 1$

Now substitute the value of u. We get:

$\rm: \longmapsto {x}^{2013} = 1$

$\rm: \longmapsto x = 1$

Therefore:

$\rm: \longmapsto {x}^{2022} + \dfrac{1}{ {x}^{2022} } = 1 + 1$

$\rm: \longmapsto {x}^{2022} + \dfrac{1}{ {x}^{2022} } = 2$

★ Which is our required answer.

$\textsf{\large{\underline{More To Know}:}}$

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)³ = a³ + 3ab(a + b) + b³

(a - b)³ = a³ - 3ab(a - b) - b³

a³ + b³ = (a + b)(a² - ab + b²)

a³ - b³ = (a - b)(a² + ab + b²)

(x + a)(x + b) = x² + (a + b)x + ab

(x + a)(x - b) = x² + (a - b)x - ab

(x - a)(x + b) = x² - (a - b)x - ab

(x - a)(x - b) = x² - (a + b)x + ab

6 0

3 years ago

Solve for x Plz help me !!!!

Taya2010 [7]

Answer:

x = 60.5°

Step-by-step explanation:

We use the exterior angle theorem to solve this

90 + 31 = 121

121/2 = 60.5

Thus, our answer is 60.5°

5 0

3 years ago

Read 2 more answers