How many members of the set S={x:1≤x≤100} are of the form 4n-1. I guess the answer is 25, but is there a way to prove it or show it?

Question

2bornot2b · Answer

n is an integer

mani_jha · Answer

Take the series of such numbers to be S.
The nth term of that series will be given by 4n-1.
Putting n=1,n=2 etc..you find that the series is:
3,7,11.......
This is an arithmetic progression.
4n-1<100
4n<101
n<25.25
Therefore number of terms of the series would be 25.

unklerhaukus · Answer

i was trying some sigma sum notation but i couldn't get it to work

Good answer @Mani_Jha

anonymous · Answer

{3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 
71, 75, 79, 83, 87, 91, 95, 99}
Here they are and they are 25. For proof, one proof above is right.