## Secuence and series

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
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 Quote by ArielGenesis is this a sequence or a series? 1,9,25,49,81,121
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
 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.

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## Secuence and series

 Quote by 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?.
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: $a_1, a_2, a_3, ...$
Pattern: Let f be any function such that $f(1) = a_1, f(2) = a_2, f(3) = a_3, ...$. Then the sequence is equal to f(1), f(2), f(3), ... This is in fact what you did. The function you chose was $f(x) = (2x -1)^2$. 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.

 Quote by ArielGenesis well at least then comment on my answer.
I did. Your answer was 'it could be both' and I said that it is both.

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