Find the Nth term of the following sequence?: 1, -4, 9, -16, ...

1 Answer
Aug 1, 2018

T_n=(-1)^(n+1)n^2

Explanation:

The formula for this sequence is

T_n=(-1)^(n+1)n^2
where n is the nth term

How did I get this formula?

  • If you look at the numbers, you will notice that they are all square numbers ie 2^2=4, 3^2=9 and 4^2=16
  • notice that if you consider 1 as your 1st term, then every even term is negative ie 1 is your 1st term, -4 is your 2nd term, 9 is your 3rd term and -16 is your 4th term
  • If you imagine squaring -1 ie (-1)^2, you will always get a positive 1
  • If you imagine cubing -1 ie (-1)^3, you will always get a negative 1
  • Hence, if you write (-1)^("even number"+1), you will get a negative 1 ie (-1)^(2+1)=(-1)^3=-1 ; (-1)^(4+1)=(-1)^5=-1
  • Also, if you write (-1)^("odd number"+1), you will get a positive 1 ie (-1)^(1+1)=(-1)^2=1 ; (-1)^(3+1)=(-1)^4=1

Thus, T_n=(-1)^(n+1)n^2