Find the next three terms in each geometric sequence.

$\mathbf{-}\mathbf{1}\mathbf{,}\mathbf{1}\mathbf{,}\mathbf{-}\mathbf{1}\mathbf{,}\mathbf{1}\mathbf{,}\mathbf{.}\mathbf{....}$

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

For example, thesequence2, 6, 18, 54, ... is ageometric progressionwith common ratio 3.

The ration of $2^{nd}$term and first term is called the common ratio.

The sequence: $-1,1,-1,1,\mathrm{.....}$

Each term in a geometric sequence can be expressed in terms of the first term $a_1$and the common ratio $r$. Since each succeeding term is formulated from one or more previous terms, this is a recursive formula.

First term $a_1=-1$ and the common ratio is:

$\begin{array}{c}r=\frac{a_2}{a_1}\\ =\frac{1}{(-1)}\\ =-1\end{array}$

In order to calculate the next three terms of the geometric sequence substitute $n=4,5,6$and $-1$for $a_1$into the formula $a_n=a_1{r}^{n-1}$.

Thus, next three terms of the sequence$-1,1,-1,1,\mathrm{.....}$are$-1,1,-1$.