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denpristay [2]
1 year ago
5

Use the explicit formula an= a₁ + (n-1) d to find the 500th term of the

Mathematics
1 answer:
ivanzaharov [21]1 year ago
8 0

Therefore, the 500th term of the sequence exists 3517.

<h3>How to estimate the 500th term of the sequence?</h3>

The given sequence is 24, 31, 38, 45, 52, ...

It exists an Arithmetic progression.

Here, the First term = 24

Common difference = 31 - 24 = 7

The given explicit formula for the nth term exists

an = a₁ + (n - 1)d

Where a₁ exists the first term, d exists a common difference.

Substitute a₁ = 24, d = 7 and n = 500

a(500) = 24 + (500 - 1)7

 = 24 + (499)7

 = 24 + 3493

a(500) = 3517

Therefore, the 500th term of the sequence exists 3517.

To learn more about Arithmetic progression refer to:

brainly.com/question/16982185

#SPJ2

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Which number completes the system of linear
LiRa [457]

The number that completes the System of Linear Inequalities represented by the Graph y >= 2x – 2 and x + 4y > =  is -12. Hence, x + 4y \geq -12

<h3>What is a System of Linear Inequalities?</h3>

A collection of linear inequalities in the same variables is referred to as a system of linear inequalities. Any ordered pair that fulfills all of the inequalities is the solution.

<h3>What is the calculation to prove the above assertion?</h3>

Recall that:

  • The linear equation with slope m and intercept c is given as follows.

y = mx + c

  • The formula for slope of line with points  and  can be expressed as

m = (y2 - y1)/(x2 - x1)

Given that

The orange line intersects y-axis at (0,-2), therefore the y-intercept is -2.

The orange line intersect the points that are (1,0)  and (0, -2).

The slope of the line can be obtained as follows:

m = (-2-0)/(0-1)

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The slope of the line is m = 2.

Therefore, the orange line is y \geq 2x -2

The blue line intersects y-axis at (0,-3), therefore the y-intercept is -3.

The blue line intersect the points that are (-4, -2) and  (0, -3)

The slope of the line can be obtained as follows.

m = (-3-(-2))/(0-(-4))

= (-3 + 2)/4

= - (1/4)

The slope of the line is:
m = -(1/4)

The inequalities is x + 4y \geq b passes through the point (0, -3)

(0) + 4 (-3) = b

-12 =b

Thus, -12 in is the number that completes the system. Hence, x + 4y \geq -12

Learn more about system of inequalities at;
brainly.com/question/9774970
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