Sequences, continued

Today, we learned another way to write sequences. In addition to the closed form we learned in class yesterday, we also learned the recursive definition for sequences. The recursive definition allows you to find the next number in the sequence one by one. It consists of two equations: the initial value for a (a₁= some constant) and then the equation for a_n as a function of a_n-1 (a_n= a_n-1 with some operation.)


Also, we learned how to find the sum of a sequence of terms. In the examples in the notes, the "n=" term underneath the Σ tells us the starting value for n. The term to the right of the Σ tells us the operation to preform for each sequential n value. The number above the Σ is a constant, which tells us the final value of n to include.
(In the 1st example, the number above Σ is 5. Since the operation given is n², the final number we include should be 5² = 25.)