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Source of the question: Taken from the sub-Reddit r/askmath here: https://www.reddit.com/r/askmath/comments/15ar3ne/looking_for_the_answer_to_the_following_sequence/

What is the next element of the sequence 6, 3, 4, 8, 19, 103/2?

Possible choices include 310/2, 311/2, 319/2, 325/2, 307/2.

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  • $\begingroup$ Could you add a hint? $\endgroup$
    – WOWOW
    Commented Aug 4, 2023 at 8:21
  • $\begingroup$ @WOWOW I think you could try reading what the author of the Reddit post said. Keep in mind that -the user asking the question likely doesn't know what the answer is ('looking for the answer') so they cannot add a hint, and that -the author of the post itself is likely not going to respond unless one directly asks them through Reddit. $\endgroup$
    – new Q Open Wid
    Commented Aug 4, 2023 at 15:19
  • $\begingroup$ @newQOpenWid, I didn't think of it that way $\endgroup$
    – WOWOW
    Commented Aug 4, 2023 at 20:41

1 Answer 1

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The answer is

136

Because:

$f(x) = 11x^5/240-23x^4/48+79x^3/48-x^2/48-1043x/120+27/2$

Proof:

$f(1) = 11(1)^5/240-23(1)^4/48+79(1)^3/48-1^2/48-1043(1)/120+27/2 = 6$
$f(2) = 11(2)^5/240-23(2)^4/48+79(2)^3/48-2^2/48-1043(2)/120+27/2 = 3$
$f(3) = 11(3)^5/240-23(3)^4/48+79(3)^3/48-3^2/48-1043(3)/120+27/2 = 4$
$f(4) = 11(4)^5/240-23(4)^4/48+79(4)^3/48-4^2/48-1043(4)/120+27/2 = 8$
$f(5) = 11(5)^5/240-23(5)^4/48+79(5)^3/48-5^2/48-1043(5)/120+27/2 = 19$
$f(6) = 11(6)^5/240-23(6)^4/48+79(6)^3/48-6^2/48-1043(6)/120+27/2 = 51.5$
$f(7) = 11(7)^5/240-23(7)^4/48+79(7)^3/48-7^2/48-1043(7)/120+27/2 = 136$

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  • $\begingroup$ Wow, really? Who would have known that that was the canonical answer! $\endgroup$
    – new Q Open Wid
    Commented Aug 9, 2023 at 17:31

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