Question

Please help with any of these problems ... I need serious answers ...

Answer 1

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 :)