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Question
Starting a sequence with these four items:

(2,-4);(16,-10); (54,-16);(128,-22) ...

The question is: knowing that the item (r,-130) belongs to this sequence, what is the value of "r"?

I already understood that (-4;-10;-16;-22; ...) are members of an aritmetic sequence with general expression An = -6n+2

With this I reached to the conclusion that -130 = -6n+2 will bring me to the 22nd item of the sequence.

What is troubling me is that in the partial sequence:

2;16;54;128 I can't figure out what is the 22nd item.

I will appreciate your assistance in this.
If I was not clear enough, do please  come back to me.
Thanks

The 2nd sequence is -4, -10, -16, -22 ...
After looking at this, the difference is -6.
This gives the sequence -6, -12, -18, -24 ...,
so to get to the right sequence of numbers it is -6x + 2.

Now the 1st sequence of numbers is 2, 16, 54, 128, ...
Dividing each element by 2 gives 1, 8, 27, 64, ...
This sequence of numbers should be recognized as 1^3, 2^3, 3^3, 4^3, ...

Solving the equation -6x+2 = -130 gives 6x = 132, so x = 22.

Putting 22 in gives 2 * 22^3.  Since 22*22 = 484, this is  = 2 * 22*484.
Since 22*484 = 10,648, the problem is then 2*10,648.  That is 21,296.

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks Scott for your reply, as well as for your sense of humour !

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#### Scott A Wilson

##### Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.