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

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

second term (a2):

n = 2

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

third term (a3):

n = 3

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

fourth term (a4):

n = 4

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

100th term (a100):

n = 100

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

That is the full solution.