The sequence defined by the formula an = 3n + 1 is quite straightforward to compute. Each term is generated by substituting successive integer values of n into the formula.
Let’s break it down step by step:
- For n = 1:
a1 = 3(1) + 1 = 3 + 1 = 4 - For n = 2:
a2 = 3(2) + 1 = 6 + 1 = 7 - For n = 3:
a3 = 3(3) + 1 = 9 + 1 = 10 - For n = 4:
a4 = 3(4) + 1 = 12 + 1 = 13 - For n = 5:
a5 = 3(5) + 1 = 15 + 1 = 16
Therefore, the first five terms of the sequence are: 4, 7, 10, 13, 16.
This sequence is linear, meaning the difference between consecutive terms remains constant. In this case, each term increases by 3, which is the coefficient of n in the formula. Such sequences are often used in mathematical problems related to arithmetic progressions.