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Nuetrik [128]
3 years ago
15

Can someone please help me. This is an equation for either an arithmetic or geometric sequence.

Mathematics
2 answers:
djyliett [7]3 years ago
4 0
A6 = -8
a15= -62

There are (15 - 6) terms in between, therefore 9 terms in between.
-8 to -62 ... there is a difference of 54
54 ÷ 9 = 6
Therefore it gets -6 each term.
a6 = -8, a7= -14, a8 = -20 ......




Ray Of Light [21]3 years ago
3 0
That's an arithmetic sequence. To find the rule of the sequence, we need to find the first term (a₁) and the difference of the sequence (d)

Make an equation system based on what are given by the question.
an = a₁ + d(n - 1)

a₆ = a₁ + d(6 - 1) = -8
a₆ = a₁ + 5d = -8 (first equation)

a₁₅ = a₁ + d(15 - 1) = -62
a₁₅ = a₁ + 14d = -62 (second equation)

Solve the equation to find the value of a₁ and d
Using elimination method, find the value of d from first equation and second equation
a₁ + 14d = -62
a₁ +  5d =   -8
-------------------- -   (substract)
        9d = -54
          d = -54/9
          d = -6

Using subtitution method, find the value of a₁. Subtitute d with -6 from the first equation.
a₁ + 5d = -8
a₁ + 5(-6) = -8
a₁ - 30 = -8
a₁ = -8 + 30
a₁ = 22

Determine the rule of the sequence
General rule for arithmetic sequence is
an = a + d(n - 1)

Now input the value of a₁ and d to the general rule, then simpllify.
an = a + d(n - 1)
an = 22 + -6(n - 1)
an = 22 -6n + 6
an = 28 - 6n

The rule of the sequence is 28 - 6n
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Find an equation of the line. Write the equation using function notation.
Gemiola [76]

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

y = -4x+9

Step-by-step explanation:

Given equation of line is:

4y=x-8

We have to convert the given line in slope-intercept form to find the slope of the line

So,

Dividing both sides by 4

\frac{4y}{4} =\frac{x-8}{4}\\y = \frac{1}{4}x-\frac{8}{4}\\y = \frac{1}{4}x-2

Let m1 be the slope of given line

Then

m_1 = \frac{1}{4}\\

Let m2 be the slope of line perpendicular to given line

As we know that produt of slopes of two perpendicular lines is -1

m_1.m_2 = -1\\\frac{1}{4} . m_2 = -1\\m_2 = -1*4\\m_2 = -4

The slope intercept form of line is given by:

y = m_2x+b

Putting the value of slope

y = -4x+b

to find the value of b, putting (3,-3) in equation

-3 = (-4)(3) + b\\-3 = -12 +b\\b = -3+12\\b = 9

Putting the value of b in the equation

y = -4x+9

Hence,

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

y = -4x+9

Keywords: Equation of line, slope

Learn more about equation of line at:

  • brainly.com/question/4837736
  • brainly.com/question/4805611

#LearnwithBrainly

4 0
3 years ago
33x-21x=-24+12 <br> I need help on this math problem. Thanks
lions [1.4K]
X=3. 33x-21x equals 12x. 24+12=36. 12x divided by 36 equals 3
8 0
3 years ago
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