SOLUTION: A friend of mine gave me this sequence as a riddle. Can you find a rule? 8, 12, 18, 24, 38, 60, 98, 150, Kind regards, Michael

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Question 1195913: A friend of mine gave me this sequence as a riddle. Can you find a rule? 8, 12, 18, 24, 38, 60, 98, 150,
Kind regards, Michael
Found 4 solutions by josgarithmetic, greenestamps, math_tutor2020, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
NO.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The response from the other tutor might seem a bit rude; but it is honest. We can't tell from their response whether they tried and couldn't find a rule, or whether they just knew from the start that it was pointless to try, because any rule they might have come up with might not be the "right" rule.

ALL problems like this, where we are given only a sequence of numbers without any context and are expected to find the rule, or to find the next number(s) in the sequence, are INVALID. Multiple different rules can always be found that produce any given sequence of numbers; and for any given sequence of numbers, ANY next number(s) will form a valid sequence.
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Refer the "Many Rules" section of this page
https://www.mathsisfun.com/algebra/sequences-finding-rule.html
and my response on this page
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1195799.html
for explanations as to why there often isn't one set formula to follow when it comes to problems like this. Things are too vague and there are many possibilities here.

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

        You may consider what follows as a  " solution "  or as a joke (or both) - - - on your choice. 

I separate the given sequence in triples

(1)   8, 12, 18

(2)  18, 24, 38

(3)  38, 60, 98

(4)  98, 150, x


I use first three triples as a learning base to develop a pattern; 
then I use this pattern to predict x in the last triple.


1st triple: round 12 to the closest multiple of 10. It will be 10.

            Next,  8 + 10 = 18.


2nd triple: round 24 to the closest multiple of 10: it will be 20.

            Next, 18 + 20 = 38.


3rd triple: round 60 to the closest multiple of 10: it will be 60.

            Next, 38 + 60 = 98.


So, my pattern is just developed. Now I apply it to the last triple.

            I round 150 to the closest multiple of 10: it is 150.

            Finally, to predict x, I add 98 and 150:  x = 98 + 150 = 248.    ANSWER

Solved   //   or,  in more accurate terms,  one of million possible patterns is found.




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