Identify the Sequence 9 , 14 , 19 , 24

Problem

9,14,19,24,…

Solution

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

14−9=5

19−14=5

24−19=5

2. Identify the type of sequence based on the constant difference. Since the difference d=5 is constant, this is an arithmetic sequence.

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

(a_1)=9

d=5

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

(a_n)=9+(n−1)*5

5. Simplify the expression for the general term.

(a_n)=9+5*n−5

(a_n)=5*n+4

Final Answer

Arithmetic Sequence: *(a_n)=5*n+4

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