Question

The explicit formula below describes a linear function, where n is a positive integer. f(n) = 5n +12 Which recursive formula describes the same function?

1. The  recursive formula that describes the same function is an = an+1 + 5

### Explicit formula of a function

The formula for calculating the  nth term of an arithmetic progression is expressed as:
Tn = a + (n + 1)d
where
a is the first term
d is the common difference
The recursive function is given as:
an = an+1 + d
where
d is the common difference
Given the explicit formula below describes a linear function, where n is a positive integer. f(n) = 5n +12
For the first term
f(1) = 5(1) + 12
f(1) = 17
For the second term
f(2) = 5(2) + 12
f(2) = 22
d = 22 – 17
d = 5
Substitute
an = an+1 + 5
Hence the  recursive formula that describes the same function is an = an+1 + 5