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3 years ago

HELP Find the 29th term of the arithmetic sequence: -13, -6, 1, 8,...

Mathematics

1 answer:

Brilliant_brown [7]3 years ago

7 0

Answer: so the answer is -9 + 23*7 = 152

Step-by-step explanation: a24 = a1 + (24-1)d where a1 = -9 and d = common difference ( 12-5 = 7)

Hope this helped :D

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A number is decreased by seven. Then, the new number is multiplied by 3 to get an answer of -9. What is the original number?

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Start by writing the system down, I will use $y$ to represent $f(x)$

$y=x^2-5x+3\wedge y=-3$

Substitute the fact that $y=-3$ into the first equation to get,

$-3=x^2-5x+3$

Simplify into a quadratic form ( $ax^2+bx+c=0$ ),

$x^2-5x+6=0$

Now you can use Vieta's rule which states that any quadratic equation can be written in the following form,

$x^2+x(m+n)+mn=0$

which then must factor into

$(x+m)(x+n)=0$

And the solutions will be $m,n$ .

Clearly for small coefficients like ours $5,6$ , this is very easy to figure out. To get 5 and 6 we simply say that $m=3, n=2$ .

This fits the definition as $5=3+2$ and $6=2\cdot3$ .

So as mentioned, solutions will equal to $m=3, n=2$ but these are just x-values in the solution pairs of a form $(x,y)$ .

To get y-values we must substitute 3 for x in the original equation and then also 2 for x in the original equation. Luckily we already know that substituting either of the two numbers yields a zero.

So the solution pairs are $(2,0)$ and $(3,0)$ .

Hope this helps :)

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