4 years ago

Which two numbers on the number line has an absolute value of 3?

Mathematics

1 answer:

Darya [45]4 years ago

8 0

3 and -3

hope l hlped u have a good day("

hope

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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).

Nastasia [14]

Answer:

Step-by-step explanation:

First term is 3

common difference = 15/2 divided by 3 = 5/2

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3 * (5/2)^7 = 1,831.0546875

To the nearest thousandth 1,831.055

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Step-by-step explanation:

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3 years ago

Read 2 more answers

The first five terms of a quadratic sequence are 3, 12, 25, 42, 63.

skad [1K]

Since we know the sequence is quadratic, we expect the $n$ -th term to have the general form

$x_n = an^2 + bn + c$

Plug in the first 3 known values of the sequence to form a system of equations.

$x_1 = 3 = a + b + c$

$x_2 = 12 = 4a + 2b + c$

$x_3 = 25 = 9a + 3b + c$

Eliminating $c$ gives

$(4a + 2b + c) - (a + b + c) = 12 - 3 \implies 3a + b = 9$

$(9a + 3b + c) - (a + b + c) = 25 - 3 \implies 8a + 2b = 22 \implies 4a + b = 11$

Eliminating $b$ gives

$(4a + b) - (3a + b) = 11 - 9 \implies a = 2$

Solving for $b,c$ , we get

$4a + b = 11 \implies b = 11-4\cdot2 = 3$

$a+b+c=3 \implies c=3-2-3 = -2$

So, the $n$ -th term of the sequence is

$x_n = \boxed{2n^2 + 3n - 2}$

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2 years ago