Find the Nth term of the following sequence?: 1, -4, 9, -16, ...
1 Answer
Aug 1, 2018
Explanation:
The formula for this sequence is
where
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 and4^2=16 - notice that if you consider
1 as your 1st term, then every even term is negative ie1 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 positive1 - If you imagine cubing
-1 ie(-1)^3 , you will always get a negative1 - Hence, if you write
(-1)^("even number"+1) , you will get a negative1 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 positive1 ie(-1)^(1+1)=(-1)^2=1 ;(-1)^(3+1)=(-1)^4=1
Thus,