# Determine whether the sequence {eq}\displaystyle -\frac{1}{2},\frac{1}{2}, \frac{3}{2},\frac{5}{2},\frac{7}{2},... {/eq} is arithmetic, geometric, or neither.

## Question:

Determine whether the sequence {eq}\displaystyle -\frac{1}{2},\frac{1}{2}, \frac{3}{2},\frac{5}{2},\frac{7}{2},... {/eq} is arithmetic, geometric, or neither.

## Arithmetic Sequence:

In an arithmetic sequence, the general term is denoted by {eq}{a_n} = {a_1} + \left( {n - 1} \right)d {/eq}, where n is the total number of terms, and d is a common difference. If the difference between two consecutive terms is the same (a constant value), then we can say that the given sequence is an arithmetic sequence. In an arithmetic sequence, {eq}{a_1},\;{a_2},\;{a_3},\;{a_4}..........{a_n} {/eq}, the common difference is measured as {eq}d = {a_2} - {a_1} = {a_3} - {a_2} {/eq}.

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Given Data:

• The given sequence is: {eq}- \dfrac{1}{2},\;\dfrac{1}{2},\;\dfrac{3}{2},\;\dfrac{5}{2},\;\dfrac{7}{2},\;......... {/eq}

In the given...