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+67

So the first step is to find what is 1+2+3+4+...+199+200 you can do that by having pairs of 201 so there are 100 pairs and 201x100=20100 and so there are 20100 numbers in the list.

The second step is to find the sum

and the third step is to divide the sum by the umbers. Use these hints!

As ever,

Techno

TechnobladeJul 13, 2021

+309

Answer: \(-53\)

The common difference is \(-84-9\over32-5\), which is -93/27, or \(-3\frac49\).

This means that the 23rd term is 9 \(-3\frac49\)(23-5), which is \(-53\).

Edit: I forgot to add an explanation for anything, and I'm low on time right now. See if you can understand the following:

The common difference is the \(n_{2}-n_{1}\over t_{2}-t_{1}\), where t is the term number (\(t_2\) being farther in the sequence) and \(n_{2}\) being the number that \(t_{2}\) is, and same with \(n_{1}\)and \(t_{1}\). The xth term will be \(n_{1}\)+ the common difference x (x - \(t_{1}\)).

So basically the formula for any question like that, if I am thinking correctly, and assuming all the variable are as meantioned earlier in the eplanation is:

\(n_{1}+\)\(n_{2}-n_{1}\over t_{2}-t{1} \)\(\cdot (x-t_{1})\).

WhyamIdoingthisJul 13, 2021

+309

Answer: \(0\)

Solution:

I originally tried solving this with imaginary numbers with the first equation, then gave up because I'm pretty bad at dealing with imaginary numbers, then thought about it a little bit, and thought of this answer.

a¹⁸⁸¹ + a¹⁸⁸² + a¹⁸⁸³ = a¹⁸⁸³ + a¹⁸⁸² + a¹⁸⁸¹ = a¹⁸⁸¹(a² + a + 1) = a¹⁸⁸¹ x 0 = 0

You can do the same thing twice again, except for the second time make it a to the power of 1884, 1885, and 1886, and for the third make it a to the power of 1887, 1888, and 1889.

All three give 0, so 0 + 0 + 0 = \(0\)

WhyamIdoingthisJul 13, 2021

+309

Answer: \(3\)

There are two ways to do this.

Way 1:

The number is obviously going to be small.

Guessing 1: Left side is 36

Guessing 2: Left side is 49

Guessing 3: Left side is 64

3 is the answer.

Way 2:

Way 1 would not have worked if the number was not an integer, or if it were larger. Factoring the left side gives (x+5)², and 64 = 8². So, you have x+5=8, which gives the answer x = 3.

WhyamIdoingthisJul 13, 2021

+309

Answer: \((1,-6,-32)\)

Solution:

(x-h)² can be simplified into x² - 2hx + h². Multiplying that by a gives ax² - 2ahx + ah². Adding k gives ax² - 2ahx + ah² + k. This leads to the equation:

\(x^2+12x+4=ax^2-2ahx+ah^2+k\)

Looking at the x² term shows that a must be equal to 1. This turns the equation into this:

\(x^2+12x+4=x²-2hx+h^2+k\)

Since -2hx is the only term containing x¹ on the right side, and 12x is the only one on the left side containing x¹, -2hx=12x. This means that h is equal to -6. The equation turns into the following:

\(x^2+12x+4=x^2+12x+36+k\)

Using the same logic as the previous, 36+k=4. Solving this gives k = -32.

Plugging all of this information into an ordered triple (a, h, k) gives \((1,-6,-32)\).

WhyamIdoingthisJul 13, 2021