that is,
If, as in the preceding article, a is the first term of a given series, 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.
