Question

Given the geometric sequence an = 6(5)n − 1, which of the following values for n lies in the appropriate domain for n?

n = −1

n = 1

n = 0

They all lie in the domain

Answer 1

The sequence is A(n) = 6 [5 ^ (n-1) ]

Although, the formula may be applied to negative, zero and positive numbers, it does not make sense to talk about the -1 or zero term.

Ther first term is A(1), where n = 1, then the answer should be n =1.

Answer: n = 1

Here you can see that you the formula may be applied, but this does not mean that you can do it, because n = 1 is used to define the first term.

For n = -1, A(1) = 6 [5^-2] = 6/ 5^2

For n = 0, A(0) = 6[5^-1] = 6/5

For n = 1, A(1) = 6 [5^0] = 6

For n =2, A(2) = 6 [5^1] = 6*5

For n = 3, A(3) = 6[5^2] = 6*5^2