The first step in working out the equation of a sequence is to write down the differences between the terms. These are:
2, 3, 4...
They are not equal, so we now look at the differences of the differences:
1, 1.
These are equal, so the equation begins x2/2
The sequence - x2/2 is:
6.5, 7, 7.5, 8
So the equation continues x2/2 + x/2
and so by the first term the entire equation is (x2+x+12)/2
This gives us the sequence as:
7, 9, 12, 16, 21, 27, 34...
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Oh, dude, I mean, like, if we're getting all mathy here, the next number would be 21. You just add the difference between each number, like 2, 3, 4... and then add that to the last number. But hey, who really cares about numbers, am I right?
Well, isn't that a beautiful sequence of numbers we have here? If we take a closer look, we can see that each number is increasing by a little more each time. So, if we continue that pattern, the next number after 16 would be 21. Just remember, there are no mistakes in this sequence, only happy little numbers.
Well, well, well, look at you trying to crack this little puzzle. The next number in the sequence is 21. How did I figure that out, you ask? I just added the previous two numbers together like a math wizard.
16
This is a sequence of perfect squares. 12=1, 22=4, 32=9, 42=16, 52=25. The next number is 62=36.
17?
a
It would be 16. The sequence is doubling pairs. 3 and 4 go on to be 6 and 8. 6 and 8 would go on to be 12 and 16. 12 and 16 would go on to be 24 and 32, and so on.