If (a_n=11-5n), what is the common difference of this sequence?

Correct answer: (-5)

The direct answer is option A: \(-5\). The sequence rule is \(a_n=11-5n\). In a linear general term, the coefficient of \(n\) gives the change when the term number increases by 1. We can verify this carefully. The first term is \(a_1=11-5=6\), and the second term is \(a_2=11-10=1\). Their difference is \(1-6=-5\). The third term is \(a_3=11-15=-4\), and \(-4-1=-5\) again. Thus the sequence decreases by 5 at every step. Option A is correct. Option B, 5, has the opposite sign and would describe increasing terms. Option C, 11, is the constant term in the formula, not the common difference. Option D, \(-11\), incorrectly treats the constant 11 as the changing part. Another algebraic check is \(a_{n+1}-a_n=[11-5(n+1)]-[11-5n]=-5\). A negative difference is perfectly valid; it simply means the terms move downward. The common mistake is to read the first number in the formula instead of the coefficient attached to \(n\).