Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n 1?

5,–1, –7, –13, –19, ...

f(n + 1) = f(n) + 6
f(n) = f(n +1) – 6
f(n +1) = f(n) – 6
f(n +1) = –6f(n)

Question

Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n > 1?

5,–1, –7, –13, –19, ...

f(n + 1) = f(n) + 6
f(n) = f(n +1) – 6
 f(n +1) = f(n) – 6 
f(n +1) = –6f(n)

Mercury · Answer

the sequence starts with 5 and subtracts a certain constant each time (try to figure out what that is first. if you're having trouble, simply subtract the second term - first term to figure out what the difference is)

now, in terms of sequence notation, f(n) refers to a certain term in the series, and f(n+1) is simply the next term. so a typical recursive sequence would be written as:

f(n+1) = f(n) ... and then some transformation, like +1 or *2, which describes how to get to the next term

try to apply this logic to the problem