3,4,7,10,13,16,19,22, . . . Find 10th term in series

Solution:

Sequence: 3, 4, 7, 10, 13, 16, 19, 22, 25, 28, ...

Observe that from the second term onward each term increases by 3 (common difference = 3).

• Method 1 (compute from the second term): the second term is 4 and the common difference is 3, so the 10th term = 4 + (10 - 2) × 3 = 4 + 8 × 3 = 4 + 24 = 28.

• Method 2 (use a formula): for n ≥ 2 the nth term can be written as 3n - 2. For n = 10: 3 × 10 - 2 = 30 - 2 = 28.

Answer: 28