question

\(\text{Assuming we start the sequence numbering at 1 so that }s_1 = 2\\ s_k = 2+9(k-1)\\ 227 = 2 + 9(k-1)\\ 225 = 9(k-1)\\ k -1 = 25\\ k=26\)

choice (D)

2, 11, 20, 29...
Which term in this sequence is 227?

\(\begin{array}{|rcll|} \hline & \text{difference} \\ \hline a_1=2 \\ & \color{red}9 \\ a_2=11 \\ & \color{red}9 \\ a_3=20 \\ & \color{red}9 \\ a_4=29 \\ \ldots \\ a_n =227 \\ \hline \end{array}\)

This is a Arithmetic Sequence.

\(\text{Formula:}~ \boxed{a_n=a_1 + (n-1)d,\text{ with } a_1=2\text{ and }d = 9 }\)

\(\begin{array}{ll} \text{where:}\\ & a_1~ \text{ is the first term, and} \\ & d~ \text{ is the difference between the terms (called the "common difference")} \\ \end{array} \)

\(\begin{array}{|rcll|} \hline 227 &=& 2 + (n-1)9 \\ 227 &=& 2 + 9n-9 \\ 227 &=& 9n-7 \\ 227+7 &=& 9n \\ 234 &=& 9n \\ n &=& \dfrac{234}{9} \\ \mathbf{n} & \mathbf{=} & \mathbf{26} \\ \hline \end{array}\)