Question

What is the rule for the sequence with the first four terms below?

0.5, 0.25, 0, –0.25

f(x)= 0.75-0.25x

f(x)=0.5-0.25x

f(x)= 0.75(-0.25)^x

f(x)= 0.5(0.25)^x

Answer 1

Option A is the correct answer.

Explanation:

0.5, 0.25, 0, –0.25 .....

The above series is an example of arithmetic progression.

First term of this AP, a = 0.5

Common difference, d = -0.25

We have equation for n th term = a + ( n-1)d

Substituting

equation for n th term = f(n) = 0.5 + (n-1)x -0.25

f(n) = 0.5 + (n-1)x -0.25 = 0.75 - 0.25 n

Changing n with x we will get

f(x)= 0.75-0.25x

Option A is the correct answer.

Answer 2

The answer is f(x) = .5 + (x-1) (-.25)=0.75-0.25 x