Question

Given the geometric series,-1, 3, -9, 27, ...find a10

Answer 1

We need to find the term a10 of the geometric sequence:

`-1,3,-9,27,...`

The formula to find the term an of a geometric sequence is:

`a_n=a_1\cdot r^(n-1)`

where a1 is the first term and r is the ratio between consecutive terms.

For this problem, we have:

`\begin{gathered} a_1=-1 \\ \\ r=(a_2)/(a_1)=(3)/(-1)=-3 \\ \\ n=10 \end{gathered}`

Thus, we obtain:

`a_(10)=-1\cdot(-3)^(10-1)=-1\cdot(-3)^9=-1\cdot(-19683)=19683`

Answer: 19683