Question

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

Answer 1

an = -6+n

or

an = 1 + 7(n-1)

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