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 troubles with finding 'the next number' in a sequence is that mathematics is so powerful we can find more than one Rule that works.
What is the next number in the sequence 1, 2, 4, 7, ?
Here are three solutions (there can be more!):
Solution 1: Add 1, then 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
Sequence: 1, 2, 4, 7, 13, 24, 44, .
So, we have three perfectly reasonable solutions, and they create totally different sequences.
Which is right? They are all right. And there are other solutions .
. it may be a list of the winners' numbers . so the next number could be . anything! |
Simplest Rule
When in doubt choose the simplest rule that makes sense, but also mention that there are other solutions.
Finding Differences
Sometimes 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:
The last row shows that we are always wrong by 5, so just add 5 and we are done:
Rule: xn = 2n + 5
OK, we could have worked out '2n+5' by just playing around with the numbers a bit, but we want a systematic way to do it, for when the sequences get more complicated.
Second Differences
Win palace play. In the sequence
{1, 2, 4, 7, 11, 16, 22, .} we need to find the differences .
. and then find the differences of those (called second differences), like this:
With second differences we multiply by n22 Monkey slot machine game.
In our case the difference is 1, so let us try just n22:
n: | 1 | 2 | 3 | 4 | 5 |
---|
Terms (xn): | 1 | 2 | 4 | 7 | 11 |
---|
n22: | 0.5 | 2 | 4.5 | 8 | 12.5 |
---|
Wrong by: | 0.5 | 0 | -0.5 | -1 | -1.5 |
---|
We are close, but seem to be drifting by 0.5, so let us try: n22 − n2
Wrong by 1 now, so let us add 1:
n22 − n2 + 1 | 1 | 2 | 4 | 7 | 11 |
---|
Wrong by: | 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, .
Other Types of Sequences
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Read Sequences and Series to learn about:
And there are also:
And many more!
In truth there are too many types of sequences to mention here, but if there is a special one you would like me to add just let me know.
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The 1.7.x branch of PrestaShop is the latest branch of PrestaShop, first released as a stable version in November of 2016. Read more about it here.
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It is constantly being improved upon. You can see it get better (and contribute to it!) here: https://github.com/PrestaShop/PrestaShop
Download it here!
Documentation for PrestaShop 1.7
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Versions of PrestaShop 1.7
Here are the 1.7 branch release dates:
| Release date | Announcement |
---|
PrestaShop 1.7.7.0 | December 3rd, 2020 | Blogpost |
PrestaShop 1.7.6.9 | November 16th, 2020 | Blogpost |
PrestaShop 1.7.7.0 RC1 | November 3rd, 2020 | Blogpost |
PrestaShop 1.7.6.8 | September 24th, 2020 | Blogpost |
Prestashop 1.7.7.0 Beta 2 | September 1st, 2020 | Blogpost |
PrestaShop 1.7.6.7 | July 6th, 2020 | Blogpost |
PrestaShop 1.7.6.6 | July 2nd, 2020 | Blogpost |
Prestashop 1.7.7.0 Beta 1 | May 13rd, 2020 | Blogpost |
PrestaShop 1.7.6.5 | April 20th, 2020 | Blogpost |
PrestaShop 1.7.6.4 | March 5th, 2020 | Blogpost |
PrestaShop 1.7.6.3 | January 21st, 2020 | Blogpost |
PrestaShop 1.7.6.2 | November 28th, 2019 | Blogpost |
PrestaShop 1.7.6.1 | August 26th, 2019 | Blogpost |
PrestaShop 1.7.6.0 | July 10th, 2019 | Blogpost |
PrestaShop 1.7.6.0 RC2 | July 5th, 2019 | Blogpost |
PrestaShop 1.7.6.0 RC1 | June 25th, 2019 | Blogpost |
PrestaShop 1.7.6.0 Beta 1 | May 13th, 2019 | Blogpost |
PrestaShop 1.7.5.2 | May 3rd, 2019 | Blogpost |
PrestaShop 1.7.5.1 | February 18th, 2019 | Blogpost |
PrestaShop 1.7.5.0 | December 18th, 2018 | Blogpost |
PrestaShop 1.7.5.0 RC1 | December 10th, 2018 | Blogpost |
PrestaShop 1.7.5.0 Beta 1 | November 8th, 2018 | Blogpost |
PrestaShop 1.7.4.4 | November 7th, 2018 | Blogpost |
PrestaShop 1.7.4.3 | October 3rd, 2018 | Blogpost |
PrestaShop 1.7.4.2 | July 27th, 2018 | Blogpost |
PrestaShop 1.7.4.1 | July 16th, 2018 | Blogpost |
PrestaShop 1.7.4.0 | July 4th, 2018 | Blogpost |
PrestaShop 1.7.3.4 | June 27th, 2018 | Blogpost |
PrestaShop 1.7.4.0 Beta 1 | June 13th, 2018 | Blogpost |
PrestaShop 1.7.3.3 | May 28th, 2018 | Blogpost |
PrestaShop 1.7.3.2 | May 3rd, 2018 | Blogpost |
PrestaShop 1.7.3.1 | April 10th, 2018 |
PrestaShop 1.7.3.0 | February 28th, 2018 | Blogpost |
PrestaShop 1.7.3.0 RC1 | February 19th, 2018 | Blogpost |
PrestaShop 1.7.3.0 Beta 1 | December 15th, 2018 | Blogpost |
PrestaShop 1.7.2.5 | February 21st, 2018 | Blogpost |
PrestaShop 1.7.2.4 | October 24th, 2017 | Blogpost |
PrestaShop 1.7.2.3. | October 9th, 2017 | Blogpost |
PrestaShop 1.7.2.2 | August 31st, 2017 |
PrestaShop 1.7.2.1 | August 16th, 2017 | Blogpost |
PrestaShop 1.7.2.0 | July 20th, 2017 | Blogpost |
PrestaShop 1.7.2.0 RC1 | July 4th, 2017 | Blogpost |
PrestaShop 1.7.1.2 | June 7th, 2017 | Blogpost |
PrestaShop 1.7.1.1 | April 20th, 2017 | Blogpost |
PrestaShop 1.7.1.0 | April 3rd, 2017 | Announcement, blogpost |
PrestaShop 1.7.0.6 | March 6th, 2017 | Blogpost |
PrestaShop 1.7.1.0 Beta 1 | February 27th, 2017 | Blogpost |
PrestaShop 1.7.0.5 | February 13th, 2017 | Blogpost |
PrestaShop 1.7.0.4 | January 10th, 2017 | Blogpost |
PrestaShop 1.7.0.3 | December 21st, 2016 | Blogpost |
PrestaShop 1.7.0.2 | November 28th, 2016 | Blogpost |
PrestaShop 1.7.0.1 | November 21st, 2016 |
PrestaShop 1.7.0.0
| November 7th, 2016 | Announcement, blogpost |
PrestaShop 1.7.0.0 RC3 | October 27th, 2016 | Blogpost |
PrestaShop 1.7.0.0 RC2 | October 10th, 2016 | Blogpost |
PrestaShop 1.7.0.0 RC1 | September 20th, 2016 | Blogpost |
PrestaShop 1.7.0.0 RC0
| August 29th, 2016 |
PrestaShop 1.7.0.0 Beta 3
| August 1st, 2016 | Blogpost |
PrestaShop 1.7.0.0 Beta 2
| July 18th, 2016 | Blogpost |
PrestaShop 1.7.0.0 Beta 1
| June 2nd, 2016 | Blogpost |
PrestaShop 1.7.0.0 alpha 4
| April 25th, 2016 | Blogpost |
PrestaShop 1.7.0.0 alpha 3
| April 4th, 2016
|
PrestaShop 1.7.0.0 alpha 2
| February 29th, 2016 | (internal release) |
PrestaShop 1.7.0.0 alpha 1
| February 12th, 2016 | (internal release) |