# 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# 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,