Write an explicit formula for the sequence given by the recursive definition a (1) = 1 and a (n+1) = a (n) + 7

an = - 6+n

or

an = 1 + 7 (n-1)

Step-by-step explanation:

a (1) = 1 and a (n+1) = a (n) + 7

The explicit formula is

an = a1 + d (n-1)

we know a1 = 1

Looking at a (n+1) = a (n) + 7

We are adding 7 each time so the common difference is + 7

an = 1 + 7 (n-1)

We can simplify this

an = 1 + 7n - 7

an = - 6+n

You can use either formula