Timeline for What's wrong with asking for the next term in a sequence?
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| May 11, 2018 at 7:03 | history | migrated | from math.stackexchange.com (revisions) | ||
| May 8, 2018 at 11:22 | comment | added | Mark Bennet | @FedericoPoloni For completeness, a sequence is indexed by integers so you get $(1,3), (2,5), (3,7), (4,9), (5,11)$ for the example you have given. There is an obvious candidate $l(x)=2x+1$ here and if $L(x)$ is another polynomial of degree $\le 4$ which passes through the five points then $l(x)-L(x)$ is a polynomial of degree less than $4$ with five zeros, and hence is the zero polynomial. Whence $L(x)=l(x)$. | |
| May 8, 2018 at 10:45 | comment | added | Federico Poloni | You should probably explain also how this applies to the sequences in the question. $3,5,7,9,11$ is not a sequence of pairs $(x_i,y_i)$. | |
| May 8, 2018 at 7:04 | history | answered | Mark Bennet | CC BY-SA 4.0 |