# Find the next three terms of the arithmetic sequence. {eq}\displaystyle \frac{3}{4}, \frac{1}{2}, \frac{1}{4}, ... {/eq}

## Question:

Find the next three terms of the arithmetic sequence.

{eq}\displaystyle \frac{3}{4}, \frac{1}{2}, \frac{1}{4}, ... {/eq}

## Arithmetic Sequence:

In mathematics, a sequence of numbers that consist of a constant difference between the two consecutive terms is known as the arithmetic sequence.

This constant difference is known as the common difference of the sequence and is denoted by the variable 'd'.

General representation of an arithmetic sequence-

$$a,(a+d),(a+2d),...........a+(n-1)d$$

where {eq}a {/eq} is the first term, {eq}d {/eq} is the common difference and {eq}n {/eq} is the total number of terms in the arithmetic sequence

#### nth term of the sequence

Formula-

{eq}a_{n} = a+(n-1)d {/eq}

Here {eq}a_{n} {/eq} is the nth term of the arithmetic sequence

## Answer and Explanation: 1

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The given arithmetic sequence is-

{eq}\displaystyle \frac{3}{4},\frac{1}{2},\frac{1}{4},......... {/eq}

In the given sequence-

{eq}\displaystyle...

See full answer below.