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...
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?
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.
a
It is: 34
A single number, such as 4642142824816 does not constitute a sequence.
16
My guess: 2.5
This is a sequence of perfect squares. 12=1, 22=4, 32=9, 42=16, 52=25. The next number is 62=36.
17?
16 is the next squared number.
The next number in the sequence 2, 4, 16, 64 is 256.
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.
a
92 - 18 = 72 72 - 16 = 56 56 - 14 = 42 42 - 12 = 30 30 - 10 = 20 20 is the next number in the sequence.
The next number in the sequence is... 64