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I can't figure out what will come next in the sequence $10,6,8,15,34,...$ . I am thinking everything, but cannot seem to find a pattern. Any hints please...

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    $\begingroup$ Where did this come from? $\endgroup$ Commented Jul 3, 2016 at 14:59
  • $\begingroup$ @JulianRosen You should not ask this it is cheat $\endgroup$ Commented Jul 3, 2016 at 17:06
  • 2
    $\begingroup$ Yes you are right, everything could come next in this (or any) sequence. $\endgroup$ Commented Jul 3, 2016 at 20:03
  • 2
    $\begingroup$ @JulianRosen After some searching, I have found that this question appears to have come from the State Bank of India's officer recruitment preliminary exam of July 3, 2016. $\endgroup$
    – f''
    Commented Jul 4, 2016 at 3:38
  • $\begingroup$ @f'' Yes it did come from there $\endgroup$
    – spectraa
    Commented Jul 5, 2016 at 14:16

2 Answers 2

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One possible solution: The sequence follows the pattern

$10\times 0.5+1=6$
$6\times 1+2=8$
$8\times 1.5+3=15$
$15\times 2+4=34$

The formula seems to be :

$x_{n}= x_{n-1} * \frac{n}{2}+n $
with $x_0 = 10$

So the next term is

$34\times 2.5+5=90.$

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$\left(\frac{10}2+1\right) \times 1 = 6$
$\left(\frac62+1\right) \times 2 = 8$
$\left(\frac82 + 1\right) \times 3= 15$
$\left(\frac{15}2 + 1\right) \times 4 = 34$
$\left(\frac{34}2 + 1\right) \times 5 = 90$

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    $\begingroup$ How is this any different than the other answer? $\endgroup$
    – Will
    Commented Jul 4, 2016 at 2:52
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    $\begingroup$ One fewer variable term per line $\endgroup$
    – humn
    Commented Jul 4, 2016 at 3:09
  • 3
    $\begingroup$ No decimal points in this answer $\endgroup$
    – Nayuki
    Commented Jul 4, 2016 at 3:25
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    $\begingroup$ Also not in spoiler tag. $\endgroup$
    – Zikato
    Commented Jul 4, 2016 at 6:47

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