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3 years ago

Determine whether each sequence is an arithmetic sequence. Write yes or no. Explain. 7, 10, 13, 16, ...

Mathematics

1 answer:

kvv77 [185]3 years ago

7 0

Answer:

The given sequence is an arithmetic sequence.

Step-by-step explanation:

Given sequence is:

7, 10, 13, 16, ...

Here

$a_1 = 7\\a_2 = 10\\a_3 = 13\\a_4 = 16$

In order for a sequence to be an arithmetic sequence the common difference between the consecutive terms of the sequence should be same. Common difference is denoted by d.

So,

$d = a_2 - a_1 = 10-7 = 3\\d = a_3 - a_2 = 13-10 = 3\\d = a_4-a_3 = 16-13 = 3$

As we can see that the common difference is same for consecutive terms.

The given sequence is an arithmetic sequence.

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Line GH contains points G(–2, 6) and H(5, –3). What is the slope of ?

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3 years ago

Can someone help me find the missing side length!

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Answer:

Step-by-step explanation

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2 years ago

Read 2 more answers

You saved $300 to spend over the summer. You decide to budget $50 to spend each week.

Oduvanchick [21]

Answer:

Part c)

The Slope of the line is: m=-50 and represents the amount of money spent per week.

Part d)

The y-intercept is: c=300 and represents the maximum money we have that can be spend over the weeks (i.e. our maximum budget alowed).

Step-by-step explanation:

To solve this question we shall look at linear equations of the simplest form reading:

$y = mx+c$ Eqn(1).

where:

$y$ : is our dependent variable that changes as a function of x

$x$ : is our independent variable that 'controls' our equation of y

$m$ : is the slope of the line

$c$ : is our y-intercept assuming an $x$ ⇔ $y$ relationship graph.

This means that as $x$ changes so does $y$ as a result.

Given Information:

Here we know that $300 is our Total budget and thus our maximum value (of money) we can spend, so with respect to Eqn (1) here:

$c=300$

The budget of $50 here denotes the slope of the line, thus how much money is spend per week, so with respect to Eqn (1) here:

$m=50$

So finally we have the following linear equation of:

$y= - 50x + 300$ Eqn(2).

Notice here our negative sign on the slope of the line. This is simply because as the weeks pass by, we spend money therefore our original total of $300 will be decreasing by $50 per week.

So with respect to Eqn(2), and different weeks thus various $x$ values we have:

Week 1: $x=1$ we have $y= -50 *1 + 300 = -50 +300 = 250$ dollars.