# What number goes in 28 and 35-11-60c

## Sequence of numbers

**"Intelligence is what an intelligence test measures". **

We all know these tests, which are supposed to measure our intelligence. Today we know that the intelligence of a person consists of many different components, which only together give a reasonably reliable statement about the intelligence. However, intelligence tests only ever measure a few of these components.

Test items that measure understanding of numbers are widespread. These are also very popular in application tests. It's often about that **Continuation of a sequence of numbers**.

__Example:__ Determine the next member of the sequence**3, 5, 7, ...**

Not difficult, many will think: the next link is **9**because this is the sequence of odd numbers.

However, this is not the only possibility, as it could also be a sequence of prime numbers, with the next being **11** would be (and not 9, since 9 is not a prime number).

If you think about it further, other possible sequelae could also be found, since a sequence of only 3 numbers cannot yet be determined clearly enough.

In this article a few tricks are to be shown how one can get on the track of such sequences of numbers and thereby maybe become a little more 'intelligent' in the next test.

But first we want to introduce and describe some well-known numerical sequences from mathematics.

**1st sequence of natural numbers:**

**1, 2, 3, 4, .... next number: 5**

**2nd sequence of even numbers:****2, 4, 6, 8, .... next number: 10**

**3rd sequence of odd numbers:****1, 3, 5, 7, .... next number: 9**

**4th sequence of square numbers:****1, 4, 9, 16, ... next number: 25**

**5. Sequence of prime numbers:****1, 2, 3, 5, 7, ... next number: 11**

**6. Distance numbers:****1, 2, 4, 7, 11, 16, next number: 22**

here the distances between the numbers increase by 1

**7. Fibonacci numbers:****1, 1, 2, 3, 5, 8, ... next number: 13**

In the famous Fibonacci sequence, the following numbers result from the

Sum of the two previous numbers. The interesting thing is that the quotient is

two consecutive numbers closer and closer to the value 1.61 .. which

the measure of the 'golden section' is used as a measured value in art and architecture

for a division corresponding to the ideal of beauty.

**8. Triangle numbers:****1, 3, 6, 10, 15, ... next number: 21**

The nth number results from the sum of the numbers from 1 to n.

That means the 5th number is 1 + 2 + 3 + 4 +5 = 15.

(These also correspond to the binomial coefficient n over 2)

**9. Tetrahedral numbers: ****1, 4, 10, 20, ... next number: 35**

The nth number results from the sum of the first n triangular numbers

(These also correspond to the binomial coefficient n over 3)

**10. Faculties:**

**1, 2, 6, 24, 120, ... next number: 720**

The nth number results from the multiplication of the first n numbers

E.g. the 5th number is 1 x 2 x 3 x 4 x 5 = 120.

A **algorithm **to determine the next number in a sequence of numbers assumes that the numbers in the sequence are derived from the

basic mathematical arithmetic operations (+, -, *, :). In addition, at least 3 terms of the sequence must be known.

Step 1: Find the difference between two consecutive terms and write this under the two numbers

Repeat this step until all differences are equal.

Step 2: If all the differences are equal, add the differences determined for the last numbers to the last number of

Follow and get the next number. (I.e. we reverse the steps we performed in step one)

__example__: What is the name of the next link in the sequence: 6, 8, 12, 18, 26, 36

Find the differences: 2 4 6 8 10 Repeat this step

2 2 2 2 differences are constant

Find the next term: 36 + 10 + 2 = **48**

If one does not obtain a constant sequence of differences in the way described above, one can try to obtain a constant sequence by dividing two consecutive terms:

__Example:__ What is the name of the next link in the sequence: 2, 4, 12, 48, ...

We divide 2 3 4 now we apply subtraction:

1 1 we reverse the steps:

The next term is: 1 + 4 = 5, 5 * 48 = **240**

The basic arithmetic operations alternate with some sequences of numbers. Example: 2, 5, 10, 13, 26, ...

Here 3 is alternately added and then multiplied by 2. Here you can apply the algorithm described above to every 2nd element.

But there are also other sequences of numbers for which the algorithm does not help. One such is, for example, the sequence of prime numbers shown above (No. 5). In the following of this type, however, only a certain basic mathematical knowledge helps to recognize relationships.

Nevertheless, most number sequences from so-called intelligence tests can be solved with the algorithm shown above.

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