# How do I solve 5 6 8

### What's next?

Often times math is about recognizing a pattern or principle. And then continue.

Can you continue this pattern?

The sequel looks like this:

So it always comes **4** Circles to it.

Write down the number of circles as numbers. Then that's one **Sequence of numbers**.

$$1, 5, 9, …$$

You can get from one number to the next by calculating $$ + 4 $$.

Now you can easily determine how many circles each continuation of the pattern has without having to draw and count all the circles.

Example: How many circles does the 7th continuation of the pattern have?

Complete the sequence of numbers up to the 7th digit. Always calculate $$ + 4 $$.

$$1, 5, 9, 13, 17, 21, 25, …$$

The 7th pattern we are looking for consists of 25 circles.

A set of numbers in a fixed order is called **Sequence of numbers**.

### Another pattern

And a little more difficult: can you continue this pattern?

The next pattern looks like this:

And the next but one like this:

A row is always added and the row has one more space than before.

You can get from one picture to the next like this: $$ +2, +3, +4, +5, $$ etc.

The sequence of numbers is: $$ 1, 3, 6, 10, 15,… $$

### Without pictures

You guessed it: you don't need any pictures to recognize patterns. You can also see patterns in rows of numbers. :)

**Example 1:**

Continue the sequence of numbers: $$ 10, 20, 30, 40,… $$

You can already see: There are always 10 added.

The sequence of numbers continues with: $$ 50, 60, 70,… $$

**Example 2:**

Continue the sequence of numbers: $$ 3, 6, 9,… $$

$$ 3 $$ are always added.

Continue the sequence of numbers: $$ 12, 15, 18,… $$

**Example 3:**

Now it's getting harder. Continued this sequence of numbers: $$ 17, 19, 23, 29,… $$

The numbers get bigger, you probably add up. Write down the additions:

The number that is added is always two greater than the number in front of it. The next step is to calculate $$ + 8 $$, then $$ + 10 $$ etc.

Continue the sequence of numbers: $$ 37, 47, 59… $$

**Example 4:**

Continue the sequence of numbers: $$ 25, 50, 54, 49, 98, 102, 97, 194, ... $$

Oh, here the numbers get bigger and smaller. In any case you need several arithmetic symbols, there is probably a minus.

Try to find out how to get from one number to another:

This is how you form the sequence of numbers: $$ * 2 $$, $$ + 4 $$, $$ - 5 $$ and then all over again $$ * 2 $$, $$ + 4 $$, $$ - 5 $$.

Continue the sequence of numbers: $$ 198, 193, 386 ... $$

You can form number sequences with all possible arithmetic operations such as $$ +, -, * ,: $$. Sequences of numbers can start with any number.

### That's interesting

Did you know that all the seeds of the sunflower lie in a certain pattern, a spiral, in the flower?

You can count the number of spirals by going to the left in the sunflower. Or you can count the number of spirals by going to the right in the sunflower. There come out 2 different numbers. Sounds crazy, huh?

Even crazier that the numbers of the spirals are not all possible numbers, but always very specific. Namely these numbers here:

$$1-1-2-3-5-8-13-21-34-55-89 …$$

The most common are sunflower blossoms with 34 (right) and 55 (left) spirals.

Image: Perspective (P. Frischknecht)

This is also the case with pine cones, pineapples, daisies and many other plants.

By the way, this sequence of numbers is called **Fibonacci**-Episode; named after **Leonardo Fibonacci** (1170 - 1240).

Spoken: Fibonachi

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