Identify the Sequence 5 , 8 , 11 , 14

Problem

5,8,11,14,…

Solution

1. Calculate the differences between consecutive terms to determine if the sequence is arithmetic.

8−5=3

11−8=3

14−11=3

2. Identify the common difference d and the first term (a_1)

d=3

(a_1)=5

3. Apply the formula for the nth term of an arithmetic sequence, (a_n)=(a_1)+(n−1)*d

(a_n)=5+(n−1)*3

4. Simplify the expression for the general term.

(a_n)=5+3*n−3

(a_n)=3*n+2

Final Answer

Arithmetic Sequence: *(a_n)=3*n+2

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