Question

Which sequence is generated by the function f(n + 1) = f(n) – 2 for f(1) = 10?

Answer 1

F(n+1)=f(n)-2 is the recursive function for this arithmetic sequence.  The explicit form is:

f(n)=a-d(n-1)  where a(initial term) is 10 and d(common difference) is -2

f(n)=10-2(n-1)  which cleans up to

f(n)=12-2n  so the first few terms are:

10,8,6,4,2,0,-2,-4.....