# What is the {eq}5th {/eq} term, {eq}10th {/eq} term and {eq}100th {/eq} term for the following sequence? {eq}5,3.9,2.8,1.7,... {/eq}

## Question:

What is the {eq}5th {/eq} term, {eq}10th {/eq} term and {eq}100th {/eq} term for the following sequence?

{eq}5,3.9,2.8,1.7,... {/eq}

## Arithmetic Sequence

An arithmetic sequence is a sequence of numbers such that the difference of any two successive numbers of the sequence is a constant.

For example, the sequence {eq}\{1, 3, 5, 7, \cdots\} {/eq} is an arithmetic sequence. The first term is {eq}a = 1 {/eq}, and the common difference between any two consecutive numbers is {eq}d = 2 {/eq}.

In general, if the first term of the sequence is {eq}a {/eq} and the common difference is {eq}d {/eq} than the terms of the sequence are {eq}x_1=a, x_2 = a+d, x_3 = a+2d, x_4 = a+3d, \cdots {/eq}.

In general, the {eq}n {/eq}th term is of the form {eq}x_n = a+(n-1)d {/eq}.

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The given sequence, {eq}\{5,3.9,2.8,1.7, \cdots\} {/eq} is an arithmetic sequence. The first term is {eq}a = 5 {/eq} and the common difference is...