Find the 82nd term of the arithmetic sequence -8, 9, 26, ...

1 answer:

4 0

The 82nd term would be 1,369.
First we need to find an equation to represent this sequence, which we can do by finding the common difference between terms and then comparing those multiples to the sequence.
To find the common difference we simply need to do 9 - -8 = 17, and this is the same as 26 - 9 = 17, so we know that it will be the same for the whole sequence.
Then we can write multiples of 17 above the original sequence and find the difference:
17, 34, 51
-8, 9, 26
The difference between 17 and -8 is -25, so our final equation becomes:
17n - 25
Then we just substitute in 82 as n because we’re looking for the 82nd term and we get 17(82) - 25 = 1394 - 25 = 1369
I hope this helps!

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(x+16)²=12 plz help me and show work

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Answer:

The answer is $x=-16$ ± $2\sqrt{3}$ in exact form or $x=-12.535898$ , $x=-19.464102$ in decimal form.

Step-by-step explanation:

To solve this problem, start by moving all terms to the left side of the equation and simplify. Simplify the equation by subtracting 12 from both sides of the equation and squaring $x+16$ , which will look like $x^{2} +32x+256-12=0$ . Next, simplify the equation again, which will look like $x^{2} +32x+244=0$ .

Then, use the quadratic formula to find the solutions. The quadratic formula looks like $\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}$ .

For this problem, the quadratic variables are as follows:

$a=1$

$b=32$

$c=244$

The next step is to substitute the values $a=1$ , $b=32$ , and $c=244$ into the quadratic formula and solve. The quadratic formula will look like $\frac{-32(+-)\sqrt{32^2-4(1*244)} }{2*1}$ . To simplify the equation, start by simplifying the numerator, which will look like $x=\frac{-32(+-)4\sqrt{3} }{2*1}$ . Then, multiply 2 by 1 and simplify the equation, which will look like $x=-16(+-)2\sqrt{3}$ . The final answer is $x=-16$ ± $2\sqrt{3}$ in exact form. In decimal form, the final answer is $x=-12.535898$ , $x=-19.464102$ .