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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}.

Answer and Explanation: 1

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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...

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Writing Rules for Arithmetic Sequences

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Chapter 9 / Lesson 7
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Understand what an arithmetic sequence is and discover how to solve arithmetic sequence problems using the explicit and recursive formulas. Learn the formula that explains how to sum a finite number of terms of an arithmetic progression.


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