# Give an explicit formula for the nth term of the following sequence. 9/10, -81/19, 729/28,...

## Question:

Give an explicit formula for the nth term of the following sequence.

{eq}\frac{9}{10}, - \frac{81}{19}, \frac{729}{28}, - \frac{6561}{37}, \frac{59049}{46}, ... {/eq}

## The Explicit Formula for the nth Term:

A sequence can be explicitly expressed as the formula for its nth term. This formula can be written by observing the pattern of the sequence or by using the formulae of the arithmetic and geometric sequences.

## Answer and Explanation: 1

Let the given sequence be {eq}S {/eq}, then we have:

{eq}S = \dfrac{9}{10}, - \dfrac{81}{19}, \dfrac{729}{28}, - \dfrac{6561}{37}, \dfrac{59049}{46}, ... {/eq}

We observe that the numerator of the fraction in each term is in the form of {eq}-(-9)^{n} {/eq} and the denominator is in the form of {eq}9n+1 {/eq}, where {eq}n {/eq} is from {eq}1 {/eq} to {eq}\infty {/eq}.

Thus, the required explicit formula for the {eq}n^{th} {/eq} term of the given sequence is:

{eq}\boxed{ S = -\dfrac{(-9)^{n}}{9n+1} } {/eq}.

#### Learn more about this topic:

from

Chapter 3 / Lesson 8What is an explicit formula for a sequence of numbers? Learn about the definition of explicit formula and how to find an explicit formula for arithmetic and geometric sequences, including examples.