SOLUTION: how do you find the recursive formula and the indicated term of this sequence 1,5,14,30,55,91?

Notice that:

to get from 1 to 5 you have to add 4, then
to get from 4 to 14 you have to add 9, then
to get from 14 to 30 you have to add 16, then
to get from 30 to 55 you have to add 25, then
to get from 55 to 91 you have to add 36.

Notice that we are always adding perfect squares.  So,
if we wanted the next term, we'd just add 91 plus
the next perfect square 49, and get 91 + 49 = 140.

We start with the first term of 1, 
then we add 2² to the 1st term to get the 2nd term,
then we add 3² to the 2nd term to get the 3rd term,
then we add 4² to the 3rd term to get the 4th term,
then we add 5² to the 4th term to get the 5th term,
then we add 6² to the 5th term to get the 6th term,

So the recusive formula is just a rule that
tells what we start with, a1, and what we do each time
to get the next term, an+1, from the preceding term.
So the recursion formula is:

a1=1.  an+1=an+(n+1)², for n≧1.

Edwin