Question

The first four terms of a sequence are shown below.

–11, –13, –15, –17, ...
Which function represents this sequence?
A. an = –2n – 11
B. an = –2n – 9
C. an = 2n – 9
D. an = 2n – 11

Answer 1

The correct function that represents the given arithmetic sequence is B. an = -2n - 9, derived by identifying the pattern of a constant difference of -2 between terms and using the formula for the nth term of an arithmetic sequence.

Step-by-step explanation:

The sequence given is arithmetic, meaning that there is a common difference between consecutive terms. To find the function that represents this sequence, we examine the pattern and notice that each term decreases by 2. Now, we look for the expression that matches the sequence at various terms (n).

• First term (n=1): -11
• Second term (n=2): -13 (-11 - 2)
• Third term (n=3): -15 (-11 - 2 - 2)
• Fourth term (n=4): -17 (-11 - 2 - 2 - 2)

Each term an can be expressed as the first term plus the common difference times (n-1), that is an = a1 + d(n-1). By substituting the values from the sequence, we get an = -11 + (-2)(n-1). Simplifying this gives an = -11 -2n + 2, which leads to an = -2n - 9 when combined. Thus, the correct function that represents this sequence is B. an = -2n - 9.