Identify the Sequence 1 , 4 , 7 , 10

Problem

1,4,7,10,…

Solution

1. Calculate the differences between consecutive terms to determine if there is a common difference.

4−1=3

7−4=3

10−7=3

2. Identify the type of sequence based on the constant difference. Since the difference d=3 is constant, this is an arithmetic sequence.

3. Determine the first term (a_1) and the common difference d

(a_1)=1

d=3

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

(a_n)=1+(n−1)*3

5. Simplify the expression for the general term.

(a_n)=1+3*n−3

(a_n)=3*n−2

Final Answer

Arithmetic Sequence: *(a_n)=3*n−2

Want more problems? Check here!