The number 115 is a term of the sequence defined by the explicit rule [tex]f(n) = 4n + 7[/tex]. Assuming that the domain of the function is the set of whole numbers greater than 0, explain how you can find the term in the sequence that is 115.

To find the term in the sequence f(n) = 4n + 7 that equals 115, solve the equation 115 = 4n + 7 for n to get n = 27. Therefore, the 27th term is 115.

Explanation:

The student asked how to find the term in the mathematical sequence defined by the rule f(n) = 4n + 7 that equals 115, given that the domain is the set of whole numbers greater than 0. To find the specific term that equals 115, we set the function equal to 115 and solve for n:

115 = 4n + 7

Subtract 7 from both sides to isolate the term containing n:

108 = 4n

Divide both sides by 4 to solve for n:

n = 27

Therefore, the term in the sequence that is 115 occurs when n is 27. This approach to solving for a particular term in a sequence exemplifies how mathematical expressions and operations can determine positions within a sequence when given an explicit rule.

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