Question

Show that the linear function in n,that is f(n)=an+b determine an arithmetic progression,where a and b are constants

Answer 1

Answer:

The common different between any two consecutive values of f(n) is constant value 'a' which show that f(n) is the arithmetic progression.

Step-by-step explanation:

Concept:

A function is arithmetic progression if and only if the common difference between any two consecutive terms of progression determine by function is  constant.

Since we are given a and b are constant and function is following

f(n) = an + b           for all n

then

f(n+1) = a(n+1) + b       for all n + 1

And

Let Difference between f(n) and f(n+1) is d then

d = f(n+1) - f(n) = a(n+1) + b - (an + b)

  = an + a + b - an - b = a                      

Thus

d = a              for all n

So the common different between any two consecutive values of f(n) is constant value 'a' which show that f(n) is the arithmetic progression.