Question

For the AP 5, 8, 11, ..., find the 20th term and the sum of the first 20 terms.

Solution

1. The first term is a = 5 and the common difference is d = 8 - 5 = 3.
2. The nth term is a + (n - 1)d, so the 20th term is 5 + 19 x 3 = 62.
3. The sum of n terms is n/2 x (first term + last term), so S20 = 20/2 x (5 + 62) = 10 x 67 = 670.
4. Therefore, the 20th term is 62 and the sum of the first 20 terms is 670.