Identify the Sequence 16 , 20 , 24 , 28

Problem

16,20,24,28,…

Solution

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

20−16=4

24−20=4

28−24=4

2. Identify the type of sequence based on the constant difference. Since the difference between terms is constant, this is an arithmetic sequence.

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

(a_1)=16

d=4

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

(a_n)=16+(n−1)*4

5. Simplify the expression for the nth term.

(a_n)=16+4*n−4

(a_n)=4*n+12

Final Answer

Arithmetic Sequence: *(a_n)=4*n+12

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