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:

**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:

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.

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

Re: Next Number in the Sequence

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

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 a_{1}, a_{2}, .... then the property that *peysy* found is that a_{k} + a_{k+1} + a_{k+2} + a_{k+3} = 45 + 8k for all k >= 1. So, a_{k+3} can be expressed through previous elements as follows: a_{k+3} = (45 + 8k) - (a_{k} + a_{k+1} + a_{k+2}). For k = 4 one gets a_{k+3} = a_{7} = 77 - a_{4} - a_{5} - a_{6} = 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.

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.