Question

How can you represent the terms of a sequence explicitly? How can you represent them recursively? Provide mathematical examples to support your opinions.

Answer 1

1/Explicitly: with a formula that contains and uses n, the term number.
Example. The sequence 9, 12, 15, 18.......... can be represented by the formula an = 3n + 6.
2/Recursively: with a formula containing and using a(n-1), the previous term.
Example: 9, 12, 15, 18...........can be represented by the formula an = a(n-1)+3. The first term (a1) needs to be specified (a1 = 9)