Question

The first four terms of a sequence are shown below 9,5,1,-3

Which of the following functions best defines this sequence?
A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1

B. f(1)=9, f(n+1)=f(n)+4 for n> or equal to 1

C. f(1)=9, f(n+1)=f(n)-5 for n> or equal to 1

D. f(1)=9, f(n+1)=f(n)+5 for n> or equal to 1

Answer 1

A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1

Explanation:

Given the sequence:

• 9, 5, 1, -3

We can easily calculate the difference of terms:

• -3- 1= 1- 5= 5-9= -4

As the difference of terms is same and equal to -4, it is the AP (arithmetic progression)

This sequence can be defined In the form of function as:

• f(1)= 9, as the first term is 9
• f(n+1)= f(n)- 4, as it is decreasing function with the difference of -4
• n ≥ 1, as we count from the first term on

All the above matches the first answer choice:

• A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1