It is possible to pair up all the numbers from 1 to 70 so that the positive difference of the numbers in each pair is always the same. For example, one such pairing up is (1,2), (3,4), (5,6),….(69,70). Here the common on difference is 1. What is the sum of all such common differences.
Answers
Let me make the question simple for you.
Let us take the range as 1 to 10 and remaining conditions are the same. So, now you'll find that you cannot find pairs for common difference more than 5.
If you take common difference as 6 then not all pairs will have the same value, because it is not possible. So you can have (n/2) common differences in this case.
Now getting back to our initial question where n=70.
So, we will have n/2 i.e. 35 common differences that will satisfy the condition.
Therefore the sum of 1+2+...33+34+35 will be (35*36)/2 = 630.{Ans]
Answer:the sum of the common difference is 35,this because the numbers that are subsequent to each other give a difference of one when the difference between the numbers is calculated. Also when the subsequent numbers are grouped according to their arrangement simply implies that the total number of the numbers divided by two((70/2)=35),also the difference is 1 thus to find out the sum of the common difference we evaluate as (35x1)=35.
Step-by-step explanation:
The sum of the common differ is 35,this is because