Identify the Sequence 2 , 6 , 10 , 14

Problem

2,6,10,14,…

Solution

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

6−2=4

10−6=4

14−10=4

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

d=4

(a_1)=2

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

(a_n)=2+(n−1)*4

4. Simplify the expression for the general term.

(a_n)=2+4*n−4

(a_n)=4*n−2

Final Answer

Arithmetic Sequence: *(a_n)=4*n−2

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