Question

For the following geometric sequence, find the explicit formula.
{1, -3, 9, ...}

Answer 1

the explicit formula for given geometric sequence {1,-3,9,..} is
`a_(n)= (-3)^(n-1)`

Explanation:

We are given the series

1,-3,9,...

the common ratio is:

-3/1 = -3

9/-3 = -3

So, the common ratio in the series is -3

a₁ = 1

The formula used for geometric series is:

`a_(n)= a_(1)(r)^(n-1)`

Putting values of a₁ and r

`a_(n)= 1(-3)^(n-1)`

`a_(n)= (-3)^(n-1)`

So, the explicit formula for given geometric sequence {1,-3,9,..} is
`a_(n)= (-3)^(n-1)`