# Consider the following sequence.s_n = 2n − 1(a) Find the first three terms of the sequence whose nth term is given.s_1 = s_2 = s_3 =(b)

Consider the following sequence. ${s}_{n}=2n-1$

a) Find the first three terms of the sequence whose nth term is given.

${s}_{1}=$

${s}_{2}=$

${s}_{3}=$

b) Classify the sequence as arithmetic, geometric, both, or neither. arithmeticgeometric bothneither If arithmetic, give d, if geometric, give r, if both, give d followed by r. (If both, enter your answers as a comma-separated list. If neither, enter NONE.)

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Jayden-James Duffy

The given sequence is, ${s}_{n}=2n-1$

a)Find the first three terms of the sequence as shown below. ${s}_{1}=2\left(1\right)-1$
$=2-1$
$=1$
${s}_{2}=2\left(2\right)-1$
$=4-1$
$=3$
${s}_{3}=2\left(3\right)-1$
$=6-1$
$=5$ Therefore, ${s}_{1}=1$
${s}_{2}=3$
${s}_{3}=5$

b) The given sequence is ${s}_{n}=2n-1.$ The terms of the sequence are 1,3,5,7,... Here,

${s}_{2}-{s}_{1}=3-1$

$=2$

${s}_{3}-{s}_{2}=5-3$

$=2$

That implies, there exists a common difference between two successive numbers. So, the given sequence is an arithmetic sequence whose common difference is $d=2.$

Jeffrey Jordon