Secuence and series

ArielGenesis

is this a sequence or a series?
1,9,25,49,81,121

it could be both
9=1+8x1
25=9+8x2
49=25+8x3
and so on

1=1^2
9=3^2
25=5^2
49=7^2
and so on

Jimmy Snyder

Answer: Both. Every series is a sequence (trivial) and every sequence is a series. For example:
As a sequence a, b, c, ...
As a series a, a + (b - a), a + (b - a) + (c - b), ...

eom

ArielGenesis

hey, first of all you have to proof that 1,9,25,49,81,121 is a sequence with a pattern of some sort, or is it to obvious?

well at least then comment on my answer.

Jimmy Snyder

You didn't ask if it was a sequence with a pattern, you just asked if it was a sequence. It is. And it has a pattern. In fact all sequences have a pattern. For instance:
Sequence: [itex]a_1, a_2, a_3, ... [/itex]
Pattern: Let f be any function such that [itex]f(1) = a_1, f(2) = a_2, f(3) = a_3, ...[/itex]. Then the sequence is equal to f(1), f(2), f(3), ... This is in fact what you did. The function you chose was [itex]f(x) = (2x -1)^2[/itex]. There are other distinct functions which also have the same values at the integers. In fact I don't really know if you chose f as I described, or one of these others.

I did. Your answer was 'it could be both' and I said that it is both.