Which function describes the arithmetic sequence shown?
3, 7, 11, 15, 19, 23, ...
A) ƒ(x) = 4x − 4
B) ƒ(x) = 4x − 3
C) ƒ(x) = 4x − 2
D) ƒ(x) = 4x − 1
replace x with 1, which one gives you 3 ?
To determine which function describes the arithmetic sequence shown, we need to identify the pattern in the sequence and find a general formula for it.
Looking at the sequence: 3, 7, 11, 15, 19, 23, ...
We can observe that each term in the sequence is obtained by adding 4 to the previous term. This indicates that the common difference between consecutive terms is 4, which is a characteristic of arithmetic sequences.
Now, let's analyze the answer choices:
A) ƒ(x) = 4x − 4
B) ƒ(x) = 4x − 3
C) ƒ(x) = 4x − 2
D) ƒ(x) = 4x − 1
We can determine the correct function by plugging in the first term of the sequence (3) into each option and checking if the subsequent terms match the arithmetic sequence.
A) ƒ(1) = 4(1) − 4 = 0 ❌
B) ƒ(1) = 4(1) − 3 = 1 ❌
C) ƒ(1) = 4(1) − 2 = 2 ❌
D) ƒ(1) = 4(1) − 1 = 3 ✅
After checking the options, we find that only option D) ƒ(x) = 4x − 1 produces the correct terms for the arithmetic sequence shown.
Therefore, the correct function that describes the arithmetic sequence is ƒ(x) = 4x − 1.