The general term for the sequence 1, 3, 5, 7, 9 can be expressed using the formula: a_n = 2n – 1, where n is the position of the term in the sequence (starting from 1).
This sequence is known as the sequence of odd numbers. To understand why the formula works, let’s break it down:
- When n = 1, a_1 = 2(1) – 1 = 1
- When n = 2, a_2 = 2(2) – 1 = 3
- When n = 3, a_3 = 2(3) – 1 = 5
- When n = 4, a_4 = 2(4) – 1 = 7
- When n = 5, a_5 = 2(5) – 1 = 9
As you can see, the formula correctly generates the terms of the sequence. Thus, the general term for the sequence of odd numbers is a_n = 2n – 1.