Question

The 10th and the 20th term of an arithmetic sequence are 10 and 40, respectively. Find its 100th term.

Answer 1

a 10 = 10;
a 20 = 40;
a n = a 1 + ( n - 1) * r => 10 = a 1 + 9 * r, and, 40 = a 1 + 19 * r => 30 = 10 * r => r = 3 => a 1 = 10 - 27 => a 1 = -17;
a 100 = a 1 + 99 * r => a 100 = - 17 + 99 * 3 => a 100 = -17 + 297 => a 100 = 280.