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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.

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Comment | Thanks Scott for your reply, as well as for your sense of humour ! |

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