How to find numbers inbetween set

Question

Is there a formula to quickly figure out the number of numbers between lets say -40 to 100 that are divisible by 3?

jwang1191 · Answer

Yeah

In your example:
The first number divisible by 3 in your set would be -39 and the last would be 99
step 1: subtract largest divisible number in set by the smallest: 99 - (-39) = 138
step 2: divide the difference by the divisible number: 138 / 3 = 46
step 3: add 1: 46 + 1 = 47 total numbers between 99 and -39 that are divisible by 3

This is easy to see with small numbers
For example:
set = from 7 to 21, we need to find number of numbers divisible by 7
21- 7 = 14
14 / 7 = 2
2 + 1 = 3

mihir0710 · Answer

Yeah its called sequence & series :

Lets say u need to know how many numbers are there between 40 to 100 that are multiple of 3.

So start with first multiple of 3 after 40. In this case it is 42 
and the last multiple of 3 before 100. Its 99.
So the formula is

nth term = first term + (n-1)*d 
where d is the difference between each of the consecutive numbers. In this case it is 3
n= number of terms (which is what you are looking for)

So using above formula :
nth term is 99
first term is 42
and d is 3

So 99 = 42 + (n-1)*3
57 = (n-1)*3
n-1 = 19
n = 20

You can cross check by any other method ..

This topic is called Sequence and series which we (Indians) study in 11th grade maths...

Hit kudos if this helps!!!

How to find numbers inbetween set

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