Is 1,9,25,49,81,121 a Sequence or Series?

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In summary: As explained, every series is a sequence and every sequence is a series. The given sequence also has a pattern, as you pointed out. In summary, the given sequence 1,9,25,49,81,121 is both a sequence and a series, with a pattern of adding 8 and squaring the result.
  • #1
ArielGenesis
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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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  • #2
ArielGenesis said:
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
 
  • #3
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.
 
  • #4
ArielGenesis said:
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: [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.

ArielGenesis said:
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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FAQ: Is 1,9,25,49,81,121 a Sequence or Series?

What is the difference between a sequence and a series?

A sequence is a list of numbers or objects that follow a specific pattern or rule. A series is the sum of all the terms in a sequence. In other words, a series is the result of adding all the numbers in a sequence.

Is 1,9,25,49,81,121 a sequence?

Yes, 1,9,25,49,81,121 is a sequence. It follows the pattern of adding the square of the previous term to get the next term.

Is 1,9,25,49,81,121 a series?

No, 1,9,25,49,81,121 is not a series because it is a finite sequence and a series requires an infinite number of terms.

What is the next term in the sequence 1,9,25,49,81,121?

The next term in the sequence is 169. This can be found by adding the square of the previous term (11^2=121) to get the next term.

Can a sequence have more than one pattern or rule?

Yes, a sequence can have more than one pattern or rule. This is known as a complex or mixed sequence. For example, a sequence could follow the pattern of adding 3 to the previous term until a certain point, and then switch to multiplying by 2 to get the next term.

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