# Next Number in the Sequence

• Aug 19th 2013, 07:26 PM
helpneeded22
Next Number in the Sequence
I am reviewing a cognitive skills test and I am unable to determine the next number in given sequences. After looking at the answers, I am still unable to identify the sequences. Could someone with better cognitive skills than I, please tell me what the sequences are:

Question 1: What is the rule that has been used to produce this series?

10, 14, 11, 18, 18, 22,

The next number in the sequence is:
Spoiler:
19

Question 2:
What is the rule that has been used to produce this series?

1, 3, 9, 2, 8, 32, 3,

The next number in the sequence is:
Spoiler:
15
• Aug 19th 2013, 08:42 PM
helpneeded22
Re: Next Number in the Sequence
Well, I finally figured out #2. Basically each series is a set of 3 numbers. The first 2 numbers of the 3 numbers is multiplied by an incrementing number. (1 x 3 = 3, 3 x 3 = 9) and then (2 x 4 = 8, 8 x 4 = 32) The next number if the sequence would then be: (3 x 5 =15, 15 x 5 = 75).

I'm still stumped on #1 though.
• Aug 24th 2013, 06:37 AM
peysy
Re: Next Number in the Sequence
10+14+11+18=53
14+11+18+18=61
11+18+18+22=69
18+18+22+x=77
x=19
• Aug 31st 2013, 03:00 AM
keypoint
Re: Next Number in the Sequence
I'm still baffled soes someone want to explain the first one to me?
• Aug 31st 2013, 03:52 AM
emakarov
Re: Next Number in the Sequence
Quote:

Originally Posted by keypoint
soes someone want to explain the first one to me?

If we denote the sequence by a1, a2, .... then the property that peysy found is that ak + ak+1 + ak+2 + ak+3 = 45 + 8k for all k >= 1. So, ak+3 can be expressed through previous elements as follows: ak+3 = (45 + 8k) - (ak + ak+1 + ak+2). For k = 4 one gets ak+3 = a7 = 77 - a4 - a5 - a6 = 77 - 18 - 18 - 22 = 19.

Amazing find. I don't like such problems. though, because it is easy to write a polynomial f(x) that equals given numbers for x = 1, 2, 3, ..., 6 and equals any number for x = 7.
• Aug 31st 2013, 10:19 AM
SworD
Re: Next Number in the Sequence
True, it ultimately depends on what would be considered the "most obvious" or "least arbitrary" pattern, but that is a matter of opinion. For any given sequence of numbers like this, the next number can be anything and still satisfy what some people would consider an aesthetically pleasing pattern.