Thread: Next Number in the Sequence

1. 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

2. 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.

3. 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

4. Re: Next Number in the Sequence

I'm still baffled soes someone want to explain the first one to me?

5. Re: Next Number in the Sequence

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.

6. 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.