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Yuliya22 [10]
3 years ago
14

If you are good at sequences in math please help I am giving more points

Mathematics
2 answers:
MaRussiya [10]3 years ago
6 0

Answer:

C. is the answer.

Step-by-step explanation:

Arithmetic sequences are linear.

So their slope is the same no matter the two points you choose.

We are given the following two points:

(7,71)

(16,26)

-----------

We can find the slope by subtracting vertically here and putting y difference on top of x difference.

71-26=45

7-16=-9

The slope is 45/-9=-5.

The equation so far is

a(n)=-5n+b

To find b we will use a known point on the line like (7,71):

71=-5(7)+b

71=-35+b

Add 35 on both sides:

106=b

The equation for the nth term is

a(n)=-5n+106

Now you could expand your choices to see switch matches.

Or you could write this equation into the form presented in the choices.

a(n)=-5(n-1+1)+106

a(n)=-5(n-1)-5+106

a(n)=-5(n-1)+101

Or

a(n)=101-5(n-1)

vodka [1.7K]3 years ago
4 0

Answer:

C. 101 - 5(n - 1)

Step-by-step explanation:

d = (26 - 71)/(16 - 7)

d = -45/9

d = -5

a7 = a1 + (7-1)(-5)

71 = a1 - 30

a1 = 101

an = 101 + (n - 1)(-5)

an = 101 - 5(n - 1)

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Answer:

x = -3

General Formulas and Concepts:

<u>Pre-Algebra</u>

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Step-by-step explanation:

<u>Step 1: Define equation</u>

5(x + 4) = -2(-4 - x) + 3

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute:                                   5x + 20 = 8 + 2x + 3
  2. Combine like terms:                   5x + 20 = 2x + 11
  3. Subtract 2x on both sides:        3x + 20 = 11
  4. Subtract 20 on both sides:        3x = -9
  5. Divide 3 on both sides:              x = -3

<u>Step 3: Check</u>

<em>Plug in x to verify it's a solution.</em>

  1. Substitute:                    5(-3 + 4) = -2(-4 - -3) + 3
  2. Simplify:                        5(-3 + 4) = -2(-4 + 3) + 3
  3. Add:                              5(1) = -2(-1) + 3
  4. Multiply:                        5 = 2 + 3
  5. Add:                              5 = 5

Here we see that 5 does indeed equal 5. ∴ x = -3 is a solution of the equation.

And we have our final answer!

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