Each number in the sequence is calpengarahan a **term** (or sometimtape "element" or "member"), read Sequencpita pengukur and Seritape for a more in-depth discussion.

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## Finding Missingi Numbers

To find a missingi number, first find a **Rule** behind the Sequence.

Sometimpita pengukur we can hanya look at the numbers and see a pattern:

### Example: 1, 4, 9, 16, ?

Answer: they are Squares (12=1, 22=4, 32=9, 42=16, ...)

Rule: **xn = n2**

Sequence: 1, 4, 9, 16, **25, 36, 49, ...**

We can use a Rule to find any term. For example, the 25th term can be found by "pluggingai in" **25** wherever **n** is.

x25 = 252 = 625

How about lainnya example:

### Example: 3, 5, 8, 13, 21, ?

After 3 and 5 all the rest are the **sum of the two numbers before**,

That is 3 + 5 = 8, 5 + 8 = 13 etc, which is part of the Fibonacci Sequence:

3, 5, 8, 13, 21, **34, 55, 89, ...**

Which has this Rule:

Rule: **xn = xn-1 + xn-2**

Now apa melakukan **xn-1** mean? It meapejarakan "the previous term" as term mageri **n-1** is 1 less than term mageri **n**.

And **xn-2** meamenjadi the term sebelum that one.

Let"s try that Rule for the 6th term:

x6 = x6-1 + x6-2

x6 = x5 + x4

So term 6 equals term 5 plus term 4. We already know term 5 is 21 and term 4 is 13, so:

x6 = 21 + 13 = 34

## Many Rules

One of the troubltape with findinew york "the lanjut number" in a sequence is that mathematics is so powerful we can find more than one Rule that works.

### maafkan saya is the next mageri in the sequence 1, 2, 4, 7, ?

di sini are three solutiopagi (tdi sini can be more!):

** **

Solution 1: Add 1, kemudian add 2, 3, 4, ...

**So, 1+1**=2, 2+**2**=4, 4+**3**=7, 7+**4**=11, etc...

**Rule: xn = n(n-1)/2 + 1**

Sequence: 1, 2, 4, 7, **11, 16, 22, ...**

(That rule looks a bit complicated, but it works)

Solution 2: After 1 and 2, add the two previous numbers, plus 1:

**Rule: xn = xn-1 + xn-2 + 1**

Sequence: 1, 2, 4, 7, **12, 20, 33, ...**

Solution 3: After 1, 2 and 4, add the three previous numbers

**Rule: xn = xn-1 + xn-2 + xn-3**

Sequence: 1, 2, 4, 7, **13, 24, 44, ...**

So, we have three perfectly reasonable solutions, and they create totally berbeda sequences.

Which is right? **They are all right.**

... It may be a list of the winners" numbers ... So the lanjut number bisa be ... Anything! |

## Simplest Rule

When in doubt choose the **simplest rule** that makpita pengukur sense, but tambahan mention that tdi sini are other solutions.

## Findingai Differences

Sometimtape it helps to find the **differences** between each pair of numbers ... This can often reveal an underlying pattern.

here is a simple case:

The differences are always 2, so we can guess that "2n" is part of the answer.

Let us try **2n**:

n: 1 2 3 4 5 kapak (xn): 2n: Wrongai by:

7 | 9 | 11 | 13 | 15 |

2 | 4 | 6 | 8 | 10 |

5 | 5 | 5 | 5 | 5 |

The terakhir row shows that we are alcara wrong by 5, so hanya add 5 and we are done:

Rule: xn = 2n + 5

OK, we bisa have worked out "2n+5" by just playingi around with the numbers a bit, but we want a **systematic** way to do it, for when the sequenctape get more complicated.

## Second Differences

In the sequence **1, 2, 4, 7, 11, 16, 22, ... **we need to find the differencpita ...

... And then find the differencpita of **those** (called second differences), liusai this:

The **second differences** in this case are 1.

With second differences we multiply by *n2***2**

In our case the difference is 1, so let us try hanya *n2***2**:

n: 1 2 3 4 5

**kapak (xn):**

*n2*

**2**: Wrong by:

1 | 2 | 4 | 7 | 11 |

0.5 | 2 | 4.5 | 8 | 12.5 |

0.5 | 0 | -0.5 | -1 | -1.5 |

We are close, but seem to be drifting by 0.5, so let us try: *n2***2** − *n***2**

*n2*

**2**−

*n*

**2**Wrong by:

0 | 1 | 3 | 6 | 10 |

1 | 1 | 1 | 1 | 1 |

Wrongai by 1 now, so let us add 1:

*n2*

**2**−

*n*

**2**+ 1 Wrong by:

1 | 2 | 4 | 7 | 11 |

0 | 0 | 0 | 0 | 0 |

We did it!

The formula ** n22 − n2 + 1** can be simplified to

**n(n-1)/2 + 1**

So by "trial-and-error" we discovered a rule that works:

Rule: **xn = n(n-1)/2 + 1**

Sequence: 1, 2, 4, 7, 11, 16, 22, **29, 37, ...Lihat lainnya: Pendaftaran Universitas Hang Tuah Surabaya 2021, Pendaftaran Universitas Hang Tuah (Uht) Surabaya**

## Other Types of Sequences

Read Sequences and Seritape to learn about:

And tdi sini are also:

And many more!

In kebenaran tdi sini are too many types of sequencpita to mention here, but if tdi sini is a special one you would lisetelah me to add just let me know.