Algebraic rules for sequences
$$
\underset{\underset{\large \text{first term}}{\large u_1}}{\LARGE 2},\underset{\underset{\large \text{second term}}{\large u_2}}{\LARGE 4},\underset{\underset{\large \text{third term}}{\large u_3}}{\LARGE 6},\underset{\underset{\large \text{fourth term}}{\large u_4}}{\LARGE 8},\underset{\underset{\large \text{fifth term}}{\large u_5}}{\underline{\phantom{\LARGE 10}}},\;\ldots\;, \underset{\underset{\large \text{general term}}{\large u_n}}{\underline{\phantom{\LARGE 2n}}},\;\ldots\;,\;\underset{\underset{\large \text{}}{\large u_{243}}}{\underline{\phantom{\LARGE 2n}}}\;,\;\ldots
$$
*Give your answer in terms of $n$.$\quad u_n=$
$$
\underset{\large u_1}{\underline{\phantom{\LARGE 22}}}\;,\;\underset{\large u_2}{\underline{\phantom{\LARGE 44}}}\;,\;\underset{\large u_3}{\underline{\phantom{\LARGE 88}}}\;,\;\underset{\large u_4}{\underline{\phantom{\LARGE 88}}}\;,\;\ldots\;, \underset{\underset{\large \text{general term}}{\large u_n}}{\LARGE 2^n},\;\ldots
$$
General Formula by Inspection
Find a formula for the general term of $2, 4, 6, 8, 10,\ldots \qquad u_n=$
Consider the sequence $3, 5, 7, 9, 11,\ldots$
What number is added to each term in $2, 4, 6, 8, 10,\ldots$ to get this sequence?
Therefore, the formula for the general term of $3, 5, 7, 9, 11,\ldots$ is $\qquad u_n=$
Consider the sequence $9, 15, 21, 27, 33,\ldots$
What number is multiplied to each term in $3, 5, 7, 9, 11,\ldots$ to get this sequence?
Therefore, the formula for the general term of $9, 15, 21, 27, 33,\ldots$ is $\qquad u_n=$
Find a formula for the general term of $1, 4, 9, 16, 25,\ldots \qquad u_n=$
Consider the sequence $2, 5, 10, 17, 26,\ldots$
What number is added to each term in $1, 4, 9, 16, 25,\ldots$ to get this sequence?
Therefore, the formula for the general term of $2, 5, 10, 17, 26,\ldots$ is $\qquad u_n=$
Consider the sequence $3, 12, 27, 48, 75,\ldots$
What number is multiplied to each term in $1, 4, 9, 16, 25,\ldots$ to get this sequence?
Therefore, the formula for the general term of $3, 12, 27, 48, 75,\ldots$ is $\qquad u_n=$
Write a formula for the general term of the sequence $\frac{1}{3}, \frac{1}{12}, \frac{1}{27}, \frac{1}{48}, \frac{1}{75},\ldots$. $\qquad u_n=$