Question

What is the closed linear form of the sequence of the odd integers starting with 1? A) an = 1 + 2n B) an = 1 - 2n C) an = -1 + 2n D) an = -1 - 2n

Answer 1

The correct closed linear form for the sequence of odd integers starting with 1 is given by the formula an = 1 + 2n, which is option A.

Step-by-step explanation:

The closed linear form of the sequence of the odd integers starting with 1 can be expressed in a mathematical function where each term an is calculated based on its position n in the sequence. For the sequence of odd numbers starting with 1, each subsequent term increases by 2. That means the first term is 1 (when n = 0), the second term is 3 (when n = 1), and so on. This pattern can be described by the formula an = 1 + 2n, making option A correct. This formula reflects the generation of odd numbers through the addition of the even increments of 2 to the initial odd number 1.