Page:Elementary algebra (1896).djvu/439

421 Rh that is,

If, as in the preceding article, a is the first term of a given series, $$d_1, d_2, d_3, \ldots$$ the first terms of the successive orders of differences, the sum of n terms of the given series is obtained from the formula

Ex. 1. Find the 7th term and the sum of the first seven terms of the series 4, 14, 30, 52, 80, .....

The successive orders of differences are

10, 16, 22, 28, 6, 6, 6, 0, 0.

Here n = 7, and a = 4.

Hence, using formula, Art. 524, the 7th term = 4 + 6. 10 + {6 5} {1 2}.6 = 154.

Using formula. Art. 525, the sum of the first seven terms

= 7, 4 + — . 10 + llAll. 6 = 448. 1.2 1.2.3

Ex. 2. Find the general term and the sum of n terms of the series

12, 40, 90, 168, 280, 432, ....

The successive orders of difference are

28, 50, 78, 112, 152, ... 22, 28, 34, 40, ... 6, 6, 6, ... 0, 0,...

Hence the nth term [Art. 524]

= n^3 + 5 n^2 + 6 n.