Which expression is an explicit rule for a mathematical sequence?

Which expression is an explicit rule for a mathematical sequence?

• A. y = x + 2
• B. y = x - 2
• C. y = -2x
• D. y = x^2 + 2

Answer: (A)

An explicit rule for a sequence gives the nth term directly as a function of its position in the sequence. The expression y = x + 2 uses the position x and adds 2, so as you move to the next term (increase x by 1), y increases by 1. For x = 1, 2, 3, you get 3, 4, 5, …, showing a clear, direct relationship between term number and value. This matches the idea of an arithmetic sequence with a constant difference of 1, starting at 3. The other forms describe different sequences (different starting values, growth rates, or nonlinear behavior), but they are not the straightforward, simple rule that maps position to value in the same way.

An explicit rule for a sequence gives the nth term directly as a function of its position in the sequence. The expression y = x + 2 uses the position x and adds 2, so as you move to the next term (increase x by 1), y increases by 1. For x = 1, 2, 3, you get 3, 4, 5, …, showing a clear, direct relationship between term number and value. This matches the idea of an arithmetic sequence with a constant difference of 1, starting at 3. The other forms describe different sequences (different starting values, growth rates, or nonlinear behavior), but they are not the straightforward, simple rule that maps position to value in the same way.