Answer:
f(3)=0, f(4)=-60
f(n) = f(n-1) + (-60)
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)