# Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises - Page 607: 29

The first five terms are: $a_1 = \dfrac{1}{3}$ $a_2 = \dfrac{1}{5}$ $a_3 = \dfrac{1}{7}$ $a_4 = \dfrac{1}{9}$ $a_5 = \dfrac{1}{11}$ The sequence has no common difference so it is not arithmetic.

#### Work Step by Step

Find the first five terms by substituting 1, 2, 3, 4 and 5 to $n$ in the given formula. $a_1 = \dfrac{1}{1+2(1)} = \dfrac{1}{1+2}=\dfrac{1}{3}$ $a_2 = \dfrac{1}{1+2(2)} = \dfrac{1}{1+4}=\dfrac{1}{5}$ $a_3 = \dfrac{1}{1+2(3)} = \dfrac{1}{1+6}=\dfrac{1}{7}$ $a_4 = \dfrac{1}{1+2(4)} = \dfrac{1}{1+8}=\dfrac{1}{9}$ $a_5 = \dfrac{1}{1+2(5)} = \dfrac{1}{1+10}=\dfrac{1}{11}$ A sequence is arithmetic if there exists common difference among consecutive terms. The sequence has no common difference so it is not arithmetic.

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