Question 240496: How can you know how many number there are in a given sequence?
For example from 1 to 100, there are 100 numbers
From 100 to 1000 there are 901 numbers(I know because my teacher tells me)
How can you know right away how many numbers there are?
Please explain a little bit carefully! Thanks for your helps!
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! In general, the formula is: last - first + 1.
To understand this, let's look at the example you gave: How many numbers from 100 to 1000?- First, how many numbers are there from 1 to 1000? Clearly (I hope) there are 1000 numbers.
- Of the numbers from 1 to 1000, which ones are not included in the numbers from 100 to 1000? Again I hope it is clear that 1 through 99 are not included.
- The number of numbers from 100 to 1000 would be the number of numbers of 1 to 1000 minus the number of numbers from 1 to 99: 1000 - 99 = 901.
Let's look at a general case. Let L = the last (or highest number) and F = the first (or lowest number in the sequence. That makes (F-1) the highest number that is not in the sequence.
Therefore the number of numbers in the sequence will be: the number of numbers from 1 to L (which is L) minus the number of numbers from 1 to (F-1) (which is (F-1):
L - (F-1) = L - F + 1
which is the formula I gave you at the beginning.
Here's an example: How many numbers are there from 536 to 2349? Answer: 2349 - 536 + 1 = 1814
I hope this helps.
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