#2 486
#3 25
#4 25
#5 1,000,000
Step-by-step explanation:
Sequences like this always have some rule that determines the next number, a pattern that needs to be followed. Sometimes the pattern is easy to find, sometimes really hard.
#2 One of the first things to check is the ratio of adjacent numbers. Here we have 2 then 6 then 18 then 54 etc.
The most prominent feature of these numbers is that the next number is always three times bigger than the previous. It's safe to assume that the missing number will be 162 • 3 = 486.
#3 Of course numbers can be arranged in the decreasing order as well. However, that does not change their ratio. In this example, carefully examining, we can see that each number in the sequence is exactly twice smaller than the previous:
800 -> 400 -> 200 -> 100 etc.
Following this pattern, we can say that the next number will be 50 / 2 = 25.
#4 Of course, ratio is not the only way to help us find the pattern. One of the very often used methods is also the difference between adjacent numbers. Let's subtract each adjacent pair:
4 - 1 = 3
9 - 4 =5
16 - 9 = 7
Longer the sequence is, greater are the chances to see the pattern, but from this we could conclude that the difference between adjacent numbers is always an odd number (3, 5, 7). We could say that the next odd number is 9, so the missing number is 16 + 9 = 25
There is another pattern that could be found. This sequence could also represent the sequence of squared numbers:
1^2, 2°2, 3°2, 4^2
In this case, the next number would be 5^2 which is also 25.
#5 Again, we can find a pattern established on the ratio of numbers, but this time with repetitive symbol L. After every L, the number is a thousand times bigger than the previous number:
0.001 -> 1 -> 1000
So, following this pattern, the missing number would be 1000 • 1000 which equals to 1000000 (a million).
