Question

Write a function rule for our pattern. 84, 90, 96, 102, 108, …. You may use f(x) or the explicit formula. Use AN for the explicit formula.

Answer 1

For the given sequence, the function rule is f(x) = 84 + 6(n-1) where 'n' represents the number of the term in the sequence.

Explanation:

For any given sequence, you need to first find the pattern, or relationship between the numbers. In this case, you can see that the numbers increase by six each time. The general formula for an arithmetic sequence, also called explicit formula, is a(n) = a(1) + d(n-1) where a(n) represents the term in the sequence; a(1) is the first term in the sequence; d=the common difference; and n=term number. When we plug in the values from the question a(1) = 84 and d = 6 to get our final equation.