Question

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

Answer 1

The first term of this series (a+1) is 1 and the common ratio (r) is -3.

Thus, the explicit formula is a_n = 1*(-3)^(n-1).

Must check this! suppose we try to calculate the 3rd term. Then n = 3.

a_3 = 1*(-3)^(3-1) = (-3)^2 = 9. This is correct.

Answer 2

`a_n=1\cdot (-3)^((n-1))`

Explanation:

We have been given a geometric sequence and we are asked to find the explicit formula for our given sequence.

The explicit formula of geometric sequence is in form:
`a_n=a_1\cdot r^((n-1))`, where,

`a_n=\text{nth term of sequence}`,

`a_1=\text{1st term of sequence}`,

`r=\text{Common ratio}`,

`n=\text{Number of term}`.

First of all, let us find common ratio of our given sequence by dividing one term by its previous term.

`r=(-3)/(1)=-3`

We can see that 1st term of our given sequence is 1. Upon substituting our given values in explicit form of geometric sequence we will get,

`a_n=1\cdot (-3)^((n-1))`

Therefore, the explicit formula for our given sequence is
`a_n=1\cdot (-3)^((n-1))`.