Nth term

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Revision as of 15:11, 22 June 2006 by 210.14.27.178 (Talk)
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Let d = common difference
    n = position in sequence [stays as "n" in the formula]
    k = an addend

dn + k = [value of term]

Contents

Common Difference (d)

The common difference, d, is easy to find out.

For example:

In 6, 13, 20, 27, 34, 41, 48...

The common difference is 7.

Position in Sequence (n)

In 5, 7, 9, 11, 13, 15...

11 is in Position 4. This means that on that case, n=4.

If n=4 then the term=11. Sounds good?

Kehy (k)

k is an addend.

A sequence like 3, 6, 9, 12, 15 is pretty obvious.

What makes it more challenging is when you give it a twist.

You can add -4 to every term and get -1, 2, 5, 8, 11. You can add 150 to every term and get 153, 156, 159, 162, 115.

The possibilities are endless. This is what k does.

How to Get the Formula

dn + k = ?

 ___________________________________________
|  TERM |  1  |  2  |  3  |  4  |  5  |  6  |
| VALUE |  5  | 11  | 17  | 23  | 29  | 35  |
'-------------------------------------------'
  1. Figure out the common difference
    • In this case, the common difference is 6.
    • So, we can conclude that the equation must contain: 6n + k = ?
  2. Now, how do we get k?
    • To get k, substitute n with any given. For our purpose, let's use 3.
    • We will substitute n with 3 and the question mark with the value of the third term..
      • 6(3) + k = 17
      • 18 + k = 17
      • k = -1
    • And so, we can now tell that k = -1.
    • Bearing this in mind, we can now say that the formula for this specific linear function is: 6n - 1.
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