# What will come in place of question mark 10 , 6 , 8, 15, 34 ,?

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...

• Where did this come from? – Julian Rosen Jul 3 '16 at 14:59
• @JulianRosen You should not ask this it is cheat – Adit Kirtani Jul 3 '16 at 17:06
• Yes you are right, everything could come next in this (or any) sequence. – Stig Hemmer Jul 3 '16 at 20:03
• @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. – f'' Jul 4 '16 at 3:38
• @f'' Yes it did come from there – spectraa Jul 5 '16 at 14:16

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

$34\times 2.5+5=90.$

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

• How is this any different than the other answer? – Will Jul 4 '16 at 2:52
• One fewer variable term per line – humn Jul 4 '16 at 3:09
• No decimal points in this answer – Nayuki Jul 4 '16 at 3:25
• Also not in spoiler tag. – Zikato Jul 4 '16 at 6:47