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3 years ago

Which of the following is an arithmetic sequence?

Mathematics

1 answer:

arsen [322]3 years ago

8 0

Answer:

Here are a few lists of numbers:

3, 5, 7 ...

21, 16, 11, 6 ...

1, 2, 4, 8 ...

Step-by-step explanation:

Ordered lists of numbers like these are called sequences. Each number in a sequence is called a term.

3,3,3, comma 5,5,5, comma 7,...7,...7, comma, point, point, point

\uparrow↑\uparrow \uparrow↑\uparrow \uparrow↑\uparrow

\footnotesize 1^\text{st}\text{ term}1

term1, start superscript, start text, s, t, end text, end superscript, start text, space, t, e, r, m, end text \footnotesize 2^\text{nd}\text{ term}2

term2, start superscript, start text, n, d, end text, end superscript, start text, space, t, e, r, m, end text \footnotesize 3^\text{rd}\text{ term}3

term3, start superscript, start text, r, d, end text, end superscript, start text, space, t, e, r, m, end text

Sequences usually have patterns that allow us to predict what the next term might be.

For example, in the sequence 3, 5, 7 ..., you always add two to get the next term:

\footnotesize\maroonC{+2\,\Large\curvearrowright}+2↷start color #ed5fa6, plus, 2, \curvearrowright, end color #ed5fa6 \footnotesize\maroonC{+2\,\Large\curvearrowright}+2↷start color #ed5fa6, plus, 2, \curvearrowright, end color #ed5fa6

3,3,3, comma 5,5,5, comma 7,...7,...7, comma, point, point, point

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Find the first four terms of the sequence an = 4n-6

natulia [17]

Answer:

The first four terms of the sequence are-6, -2, 2 and 6

Step-by-step explanation:

The given sequence is $a_n=4n-6$

In order to find the first four term of the sequence we put n =0, 1, 2 and 3.

For n =0

$a_0=4(0)-6=-6$

For n =1

$a_1=4(1)-6=-2$

For n =2

$a_2=4(2)-6=2$

For n =3

$a_3=4(3)-6=6$

Therefore, the first four terms of the sequence are

-6, -2, 2 and 6

5 0

3 years ago

Can you solve this problem please

Afina-wow [57]

Answer:

k = 11

Step-by-step explanation:

Given the points are collinear then the slopes between consecutive points are equal.

Using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (1, - 1)

m = $\frac{-1-1}{1-5}$ = $\frac{-2}{-4}$ = $\frac{1}{2}$

Repeat with another 2 points and equate to $\frac{1}{2}$

with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (k, 4)

m = $\frac{4+1}{k-1}$ , then

$\frac{5}{k-1}$ = $\frac{1}{2}$ ( cross- multiply )

k - 1 = 10 ( add 1 to both sides )

k = 11

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3 years ago

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balandron [24]

The graph is labeled correctly, so it is just a matter of counting the "blocks."

B) To get from Jeremy's house to the school, we need to go down 7 blocks and then 3 more blocks for a total of 10 blocks.

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Answer: 100 miles

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earnstyle [38]

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