Identify the Sequence 1 , 3 , 5 , 7

Problem

1,3,5,7,…

Solution

1. Identify the terms of the sequence as (a_1)=1 (a_2)=3 (a_3)=5 and (a_4)=7

2. Calculate the difference between consecutive terms to check for a common difference.

3. Subtract the first term from the second: 3 - 1 = 2$.

4. Subtract the second term from the third: 5 - 3 = 2$.

5. Subtract the third term from the fourth: 7 - 5 = 2$.

6. Conclude that since the difference is constant, the sequence is an arithmetic sequence with a common difference d=2 and a first term (a_1)=1

7. Determine the general formula using (a_n)=(a_1)+(n−1)*d

8. Substitute the values: (a_n)=1+(n−1)*2

9. Simplify the expression: (a_n)=2*n−1

Final Answer

Arithmetic Sequence: *(a_n)=2*n−1

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