What is the 15th term of the AP (1, 4, 7, 10, ...)?

Correct answer: 43

The governing rule for the nth term of an arithmetic progression is a_n = a + (n − 1)d. In the given AP, the first term is a = 1 and the common difference is d = 4 − 1 = 3. The 15th term is reached after 15 − 1 = 14 equal jumps from the first term. Hence a_15 = 1 + 14 × 3 = 1 + 42 = 43. Therefore option C is correct. Option B is only 14 × 3 and leaves out the initial term. Option D results from adding one extra difference, as if fifteen jumps were needed. Option A does not satisfy the sequence rule, since the terms increase by 3 each time. Remembering that the number of jumps is one less than the term number prevents the common off-by-one error.