Final answer:
The question requires using differentiation and induction to prove a property of a sequence; however, without full details, we can't provide a specific proof. An example would be differentiating a sequence's rule to find its derivative and then using induction to show the result holds for all terms in the sequence.
Step-by-step explanation:
The question seems incomplete, but it appears to involve proving a mathematical statement about sequences through differentiation and induction. Mathematical induction typically starts by proving a base case, then assuming the statement is true for an arbitrary case n, and finally proving it for the next case n+1. Differentiation is a process in calculus used to find the rate at which a function is changing at any given point.
To proceed with an actual proof, we would first need the sequence's rule or function, the property to be proven, and the base case. However, lacking the complete details of the sequence, an example could be proving that the derivative of an = n2 is an' = 2n. For this, you would differentiate an to get an' and then use induction to show it holds for all n.