2, 4, 6, 10, 16, 26...
What number is next in the sequence?
42.
The pattern is that each number is the sum of the two preceding numbers:
2 + 4 = 6
4 + 6 = 10
6 + 10 = 16
10 + 16 = 26
16 + 26 = 42
I believe this is called the "fibonacci sequence"
To find the next number in the sequence, let's analyze the pattern:
The difference between the first two numbers is 4 - 2 = 2.
The difference between the second two numbers is 6 - 4 = 2.
The difference between the third two numbers is 10 - 6 = 4.
The difference between the fourth two numbers is 16 - 10 = 6.
We can observe that the differences between consecutive pairs of numbers are increasing by 2 each time.
Therefore, to find the next number in the sequence, we add 6 + 2 = 8 to the last number in the sequence:
26 + 8 = 34.
So, the next number in the sequence is 34.
To find the next number in the sequence, let's analyze the pattern:
From 2 to 4, there is an increase of 2.
From 4 to 6, there is an increase of 2.
From 6 to 10, there is an increase of 4.
From 10 to 16, there is an increase of 6.
From 16 to 26, there is an increase of 10.
As we can see, the differences between consecutive terms in the sequence are increasing, specifically by 2, 4, 6, and 10 successively. To find the next difference, we can add the next positive integer, which is 14, to the last difference of 10. So the next difference is 10 + 14 = 24.
Now, let's find the next number in the sequence by adding the next difference to the previous number:
26 + 24 = 50
Therefore, the next number in the sequence is 50.