The beginning of an arithmetic sequence is shown below. What is the n^th term rule for this sequence?

<br />The sequence $5,7,9,11 , \ldots$ looks like the sequence $1,2,3,4 , \ldots$ except that each term is multiplied by 2 and an additional 3 is added. So, the expression that describes this sequence is $\mathbf { 2n+3 }$, where $n$ represents the position of a term in the sequence. Let's verify the first four terms:<br /><br />1. To find the $1^{st}$ term, plug in $n = 1$:<br />\[2n +3 = 2(1) + 3 = 5\]<br /> <br />2. To find the $2^{nd}$ term, plug in $n = 2$:<br />\[2n+3 = 2(2) + 3 = 7\]<br /> <br />3. To find the $3^{rd}$ term, plug in $n = 3$:<br />\[2n+3 = 2(3) + 3 = 9\]<br /> <br />4. To find the $4^{th}$ term, plug in $n = 4$. <br />\[2n+3 = 2(4) + 3 = 11\]<br /><br />Considering the explicit second-order difference and inspections for the terms, it is obvious that the sequence $5,7,9,11 , \ldots$ can be described by the rule $\mathbf { 2n + 3 }$.