Question

Recursive sequence.

Answer 1

Answer:

f(3)=0, f(4)=-60

f(n) = f(n-1) + (-60)

Step-by-step explanation:

Arithmetic Sequences

The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

f(n)=f(1)+(n-1)r

Where

f(n) = nth term

f(1) = first term

r   = common difference

n  = number of the term

The given sequence has two known terms: 120, 60, ...

The common difference is found by subtracting consecutive terms:

r = 60 - 120 = -60

Thus the next two terms are:

f(3)=120+(3-1)(-60)=120-120 = 0

f(4)=120+(4-1)(-60)=120-180 = -60

Since each term is calculated as the previous term plus -60, then the recursive formula is:

f(n) = f(n-1) + (-60)