the first term, we can thence find the common difference. Suppose, for example, the first term of a series to be one, the number of terms 100, and the sum 10,000. Since 10,000 was made by multiplying the sum of the first and last terms by ¹⁰⁰/₂, if we divide by this, we shall recover the sum of the first and last terms. Now, ¹⁰,⁰⁰⁰/₁ divided by ¹⁰⁰/₂ is (122) 200, and the first term being 1, the last term is 199. We have then to pass from 1 to 199, or through 198, by 99 equal steps. Each step is, therefore, ¹⁹⁸/⁹⁹, or 2, which is the common difference; or the series is 1, 3, 5, &c., up to
| Given. | To find. | |||
|---|---|---|---|---|
| Sum. | No. of terms. | First term. | Last term. | Common diff. |
| 1809025 | 1345 | 1 | 2689 | 2 |
| 44 | 10 | 3 | 29 | 14 |
| 5 | 45 | |||
| 7075600 | 1330 | 4 | 10636 | 8 |
- We now return to (170), in which we compared two numbers together by their difference. This, however, is not the method of comparison which we employ in common life, as any single familiar instance will shew. For example, we say of A, who has 10 thousand pounds, that he is much richer than B, who has