1.a.) find the next four terms: a8,a9,a10,a11

=0, 9, -26, 65, -124, 217, -342

1.b) find a direct formula for , [hint: you may want to look at perfect squares, perfect cubes, powers of 2, powers of

Answers:

1a) The next four terms are: 513, -728, 1001, -1330

1b) The direct formula is

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Explanation:

It helps to start with part B first. The direct formula will help us find the next four terms in a very efficient manner.

Start with the sequence {0, 9, -26, 65, -124, 217, -342}

Subtract 1 from each term to get this new sequence {-1, 8, -27, 64, -125, 216, -343}, which closely resembles the sequence {1, 8, 27, 64, 125, 216, 343}. This is the sequence of perfect cubes. The only difference is that each term alternates from positive to negative and vice versa.

So we will have an n^3 as part of the equation and also a (-1)^n as part of the equation. The (-1)^n portion allows us to alternate in signs. Put together we have (-1)^n*n^3 so far

The last thing we do is add 1 to this so that we undo the operation "subtract 1" we did earlier to the original list.

Therefore the formula is

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To help verify we have the right formula, plug in n = 1 and we get

and plug in n = 2 to get

and so on. I'll let you check the other terms

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Let's find the terms a8,a9,a10,a11

This is simply a matter of plugging n = 8, n = 9, n = 10, and n = 11

Plug in n = 8

Repeat for n = 9

Repeat for n = 10

Repeat for n = 11

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula