Question

Consider this sequence: 3,___,−6,−21 What is the explicit function that defines this sequence? If arithmetic, write the function in simplified form. If geometric, write the function with an exponent of n−1. Be sure to keep all numbers in improper tion form.

A.f(n)=4−3n
B.f(n)=−3×2ⁿ
C.f(n)=−3n−3
D.f(n)=3×(−2)ⁿ⁻¹

Answer 1

The explicit function that defines the given sequence is f(n) = -15n + 18.

Step-by-step explanation:

The given sequence is 3, ___, -6, -21. To find the explicit function that defines this sequence, we need to analyze the pattern.

Upon closer inspection of the sequence, we can observe that each term is obtained by subtracting a certain value from the previous term. Therefore, it is an arithmetic sequence.

To find the common difference, we can subtract any two consecutive terms. For example, if we subtract -6 from ___, we get a common difference of -15.

Since the first term is 3, we can use the formula for an arithmetic sequence, which is f(n) = a + (n-1)d, where a is the first term and d is the common difference. In this case, the explicit function that defines the sequence would be f(n) = 3 + (n-1)(-15), which simplifies to f(n) = -15n + 18.