# In the following geometric sequence, find an expression for (i) the 17th term; (ii) for the nth...

## Question:

In the following geometric sequence, find an expression for (i) the 17th term; (ii) for the nth term.

{eq}\displaystyle -\sqrt 5,\ 5,\ \cdots {/eq}

## Geometric Sequence:

A geometric sequence is a set of numbers where each phrase following the first is obtained by multiplying the term before it by a factor known as the common ratio (r). The sequence's first term (a) is typically provided, and the remaining terms are obtained by multiplying the first term by r.

## Answer and Explanation: 1

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$$\displaystyle -\sqrt 5,\ 5,\ \cdots $$

Finding the common ratio:

$$\begin{align} r &= \dfrac{5}{-\sqrt{5}}\\ r &= -\sqrt{5}...

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#### Learn more about this topic:

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Chapter 27 / Lesson 26Learn about geometric sequences. Understand what a geometric sequence is, learn how to find the common ratio of a geometric sequence, and see examples.