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

  • Context: High School 
  • Thread starter Thread starter ArielGenesis
  • Start date Start date
  • Tags Tags
    Series
Click For Summary

Discussion Overview

The discussion revolves around whether the sequence of numbers 1, 9, 25, 49, 81, 121 constitutes a sequence or a series. Participants explore the definitions and characteristics of sequences and series, as well as the patterns within the given numbers.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants propose that the numbers can be classified as both a sequence and a series, noting that every series is a sequence and vice versa.
  • One participant emphasizes the need to prove that the numbers form a sequence with a discernible pattern, questioning if this is too obvious.
  • Another participant asserts that the sequence does indeed have a pattern, suggesting that all sequences inherently possess patterns and providing a specific function that could represent the sequence.
  • There is a challenge regarding the interpretation of the original question, with one participant arguing that the inquiry was simply about whether it is a sequence, which they affirm it is.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of proving the pattern of the sequence, with some asserting it is obvious while others seek clarification. There is no clear consensus on the interpretation of the original question regarding the classification of the numbers.

Contextual Notes

Participants reference mathematical functions and patterns without resolving the specifics of these functions or their implications for the sequence. The discussion remains open-ended regarding the definitions and characteristics of sequences and series.

ArielGenesis
Messages
238
Reaction score
0
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
 
Mathematics news on Phys.org
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
 
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.
 
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.
 
Last edited:

Similar threads

  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 24 ·
Replies
24
Views
3K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
2
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K