Identify the Sequence 5 , 6 , 7 , 8

Problem

5,6,7,8,…

Solution

1. Identify the terms of the sequence as (a_1)=5 (a_2)=6 (a_3)=7 and (a_4)=8

2. Calculate the difference between consecutive terms to check for an arithmetic pattern.

6−5=1

7−6=1

8−7=1

3. Determine that since the difference is constant, the sequence is an arithmetic progression with a common difference d=1 and a first term (a_1)=5

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

(a_n)=5+(n−1)*(1)

5. Simplify the expression for the general term.

(a_n)=n+4

Final Answer

(a_n)=n+4

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