1) you always need to jot down your observations for these types of questions first:
1: 1
2: 5
3: 13
4. 25
They are all odd so there is probably a '+1' in the equation
5= 4+1= 2n+1 = 2(1n)+1 = 2(n(n-1))+1
13= 12+1= 4n+1 = 2(2n)+1 = 2(n(n-1))+1
25= 24+1= 6n+1 = 2(3n)+1 = 2(n(n-1))+1
Now we've established a formula. (this does work for the first one as well but the working is a bit confusing so I didn't include it.)
the 37th one would be:
2(37(37-1))+1
2(37(36))+1
2(1332)+1
2664+1
2665
(I spent a really long time on this and I might edit this with the answers to the other ones but I might fall asleep because I'm ill at the moment, anyway, here you go.)
Hope this helps :)
