An algebraic expression for the Nth term in a number sequence?

Question

The sequence is 1, 2, 4, 9, 16, 25~~~
It seems (n-1) ² does not work.

The sequence is 1, 2, 4, 9, 16, 25~~~
It seems (n-1) ² does not work

This is a question in an entrance paper for 15+ senior school student

Answer 1

1/30 n^5 - 5/8 n^4 + 53/12 n^3 -107/8 n^2 + 371/20 n - 8 works.

I don't think you'll find anything nicer.

Answer 2

a million) the series (7, 10 , 13 ,...........) is arithmetic series because of the fact T2-T1=10-7=3 & T3-T2=13-10=3 then T2-T1=T3-T2=3= consistent so that's an arithmetic series ,its the version of this A.S, its nth term is Tn=a+(n-a million)d a is the 1st term , n is style of words , d is the version Tn=7+(n-a million)*3=7+3n-3=3n+4 2)the series (8, eleven,14, ,17,................) is an arithmetic series series because of the fact T2-T1=eleven-8=3 & T3-T2=14-eleven =3 so that's an arithmetic series its nth term is Tn=a+(n-a million)d =8+(n-a million)*3=8+3n-3=3n+5