Question

a sequence is defined recursively by the formula f(n + 1) = f(n) + 3 . The first term of the sequence is –4. What is the next term in the sequence?

Answer 1

hello :
f(n + 1) = f(n) + 3
f is a arithemetic sequence of the common difference is : 3
f(1) = -4 ( the first term)
the next term in the sequence is : f(n) = f(1) +(n-1) d .. d=3
f(n) =-4+(n-1)(3)
f(n) = 3n -7

Answer 2

we have

`f(n + 1) = f(n) + 3`

we know that

`f(1)=-4`

Find the value of
`f(2)`

for
`n=1`

`f(1 + 1) = f(1) + 3`

`f(2) = f(1) + 3`

`f(2) = -4 + 3`

`f(2) = -1`

therefore

the answer is

the next term in the sequence is
`-1`