Question

For the sequence an=(−1)n3n2 ,its first term is its second term is its third term is its fourth term is its 100th term is

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

an = ((-1)^n * 3) / (n^2)

Step 02:

sequence:

first term (a1):

n = 1

`a1\text{ = }\frac{(-1)\placeholder{⬚}^1\text{ * 3}}{(1)\placeholder{⬚}^2}=((-1)3)/(1)=(-3)/(1)=-3`

second term (a2):

n = 2

`a2=\frac{(-1)\placeholder{⬚}^2*3}{(2^)\placeholder{⬚}^2}=((1)3)/(4)=(3)/(4)`

third term (a3):

n = 3

`a3=\frac{(-1)\placeholder{⬚}^3*3}{(3)\placeholder{⬚}^2}=((-1)3)/(9)=(-3)/(9)=(-1)/(3)`

fourth term (a4):

n = 4

`a4=\frac{(-1)\placeholder{⬚}^4*3}{(4)\placeholder{⬚}^2}=((1)3)/(16)=(3)/(16)`

100th term (a100):

n = 100

`a100=\frac{(-1)\placeholder{⬚}^(100)*3}{(100)\placeholder{⬚}^2}=((1)3)/(10000)=(3)/(10000)`

That is the full solution.