Recursive Sequence
A recursive sequence is a sequence in which terms are defined using one or more previous terms which are given.
If you know the nth term of an arithmetic sequence and you know the common difference, d, you can find the (n + 1)th term using the recursive formula an + 1 = an + d.
Example 1:
Find the 9th term of the arithmetic sequence if the common difference is 7 and the 8th term is 51.
If you know the nth term and the common ratio, r, of a geometric sequence, you can find the (n + 1)th term using the recursive formula. an + 1 = an · r.
Example 2:
Write the first four terms of the geometric sequence whose first term is a1 = 3 and whose common ratio is
r = 2.
