| n | ||
| S i | = | n (n+1) |
| i=0 | 2 |
An arithmetic progression is the sum of an arithmetic sequence - a list of numbers in which each term has fixed difference from the one before. So if the first term is a, and the difference is d, the sequence is:
a, a+d, a+2d, a+3d, ....
The progression is thus of the form:
a + (a + d) + (a + 2d) + (a + 3d) + ....
or
|
i=n |
|
|
S |
(a + id) |
|
i=0 |
and the total is
| 2an + | (n -1) n d |
| 2 |
An arithmetic progression is the sum of an arithmetic sequence - a list of numbers in which each term is in fixed ratio to the one before. So if the first term is a, and the difference is d, the sequence is:
a, ar, ar2, ar3, ar4 ....
The progression is thus of the form:
a + ar + ar2 + ar3 + ar4 ....
and the total is
| a (rn - 1) |
| r - 1 |
| P | = | 1 | - | 1 | + | 1 | - | 1 | + | 1 | - | 1 | + ... |
| 4 | 3 | 5 | 7 | 9 | 11 |
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