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:

$\begin{gathered} a_1=-1 \\ \\ r=\frac{a_2}{a_1}=\frac{3}{-1}=-3 \\ \\ n=10 \end{gathered}$

Thus, we obtain:

$a_{10}=-1\cdot(-3)^{10-1}=-1\cdot(-3)^9=-1\cdot(-19683)=19683$

Answer: 19683