Grade 10Algebra
Find the no. Of ways in which 3 distinct nos. Can be selected from the set{1,2,3...99,100} so that they form an AP
Find the no. Of ways in which 3 distinct nos. Can be selected from the set{1,2,3...99,100} so that they form an AP
1 Answer
Vishrut Arora
This question can be easily solved by identifying the series
consider,
AP with common difference of 1
1,2,3,....
2,3,4.....
finally 98,99,100
=> There are 98 APs possible with common difference of 1
AP with common difference of 2
1,3,5..
2,4,6...
finally 96,98,100
=> There are 96 APs possible with common difference of 2
and so on till
AP with common difference of 49
1,50,99....
2,51,100....
=> There are 2 APs with the maximum common difference possible
Now for total no.of APs u have to add 98+96+94+....2
using the formula n/2(2*a+(n-1)*d)
We finally get the answer as 2450
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algebra
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