Find the first four terms and the 100th term of the sequence whose nth term is given.

Question

Find the first four terms and the 100th term of the sequence whose nth term is given.

an =	−1
3
	n
a1	=
a2	=
a3	=
a4	=
a100	=

Answer 1

It looks like f(n) = 3 * (-1)^n

please do not use the table as it really makes it hard to read...

use parenthesis for grouping and the carrot sign ^ for the exponent

n=1 ---> f(1) = 3 * (-1)^1 = 3 * -1 = -3

n=2 ----> f(2) = 3 * (-1)^2 = 3 * 1 = 3

n=3 -----> f(3) = 3 * (-1)^3 = 3*-1 = -3

n-4 -----> f(4) = 3 * (-1)^4 = 3*1 = 3

hopefully by now you see the pattern that when n is EVEN, (-1) to the even power exponent

is 1 , so the result is 3.

Likewise, when n is ODD, (-1) to the odd power exponent is -1, so the result is -3

Then the following table can be completed.

N f(n)

1 -3

2 3

3 -3

4 3

.... ...

98 3

99 -3

100 3

101 -3