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2 years ago

Find the 53rd term of the arithmetic sequence 27,11, -5

Mathematics

1 answer:

vivado [14]2 years ago

3 0

Answer:

The 53rd term of this arithmetic sequence is -805.

Step-by-step explanation:

The general rule of an arithmetic sequence is the following:

$a_{n+1} = a_{n} + d$

In which d is the common diference between each term, that is, $d = a_{3} - a_{2} = a_{2} - a_{1}$ .

To find the nth term of the sequence, this equation can be written as:

$a_{n} = a_{1} + (n-1)d$

27,11, -5

So $a_{1} = 27, a_{2} - a_{1} = 11 - 27 = -16[/tex[tex]a_{n} = a_{1} + (n-1)d$

$a_{53} = a_{1} + (52)d = 27 + 52*(-16) = -805$

The 53rd term of this arithmetic sequence is -805.

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Step-by-step explanation:

-2a + x

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-2(-2) + 7

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Let's take the percentage as x

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3 years ago

Find all roots: x^3 + 7x^2 + 12x = 0 Show all work and check your answer.

Aliun [14]

The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4

Solution:

We have been given a cubic polynomial.

$x^{3}+7 x^{2}+12 x=0$

We need to find the three roots of the given polynomial.

Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.

This gives us:

$x^{3}+7 x^{2}+12 x=0$

$x\left(x^{2}+7 x+12\right)=0$ ----- eqn 1

So, from the above eq1 we can find the first root of the polynomial, which will be:

x = 0

Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:

$x^{2}+7 x+12=0$

we have to use the quadratic equation to solve this polynomial. The quadratic formula is:

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Now, a = 1, b = 7 and c = 12

By substituting the values of a,b and c in the quadratic equation we get;

$\begin{array}{l}{x=\frac{-7 \pm \sqrt{7^{2}-4 \times 1 \times 12}}{2 \times 1}} \\\\{x=\frac{-7 \pm \sqrt{1}}{2}}\end{array}$

Therefore, the two roots are:

$\begin{array}{l}{x=\frac{-7+\sqrt{1}}{2}=\frac{-7+1}{2}=\frac{-6}{2}} \\\\ {x=-3}\end{array}$

And,

$\begin{array}{c}{x=\frac{-7-\sqrt{1}}{2}} \\\\ {x=-4}\end{array}$

Hence, the three roots of the given cubic polynomial is 0, -3 and -4

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3 years ago

Write the equation – 2x2 + 1 = 5x in standard form

oksian1 [2.3K]

Answer: 5 x = − 3

Step-by-step explanation: brainlest please

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3 years ago