Write the recursive formula of the following sequences use the generated patterns show your solution. 1.) 3,8,13,18,23,... 2.) 12,16,20,24,28,...

To find the recursive formula for the given sequences, we need to identify the pattern and the relationship between consecutive terms.

### Sequence 1: \( 3, 8, 13, 18, 23, \ldots \)

Let's denote the sequence by \( a_n \), where \( a_1 = 3 \), \( a_2 = 8 \), and so on.

1. **Identify the pattern**: We observe that the difference between consecutive terms is constant. Specifically:
   \[
   a_2 - a_1 = 8 - 3 = 5
   \]
   \[
   a_3 - a_2 = 13 - 8 = 5
   \]
   \[
   a_4 - a_3 = 18 - 13 = 5
   \]
   The common difference is \( 5 \).

2. **Write the recursive formula**: Since each term is obtained by adding 5 to the previous term, we

Learn how to find the recursive formula for the arithmetic sequence 3, 8, 13, 18, 23, ... by identifying the constant difference between consecutive terms. This problem involves understanding arithmetic sequences and deriving the recursive formula step-by-step. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation