A sequence $< a _ { n } >$ satisfies $3 a _ { n + 1 } = a _ { n } + n$ (for all positive integers $n$) and $a _ { 1 } = 2$. Let the sequence $< b _ { n } >$ satisfy $b _ { n } = a _ { n } - \frac { n } { 2 } + \frac { 3 } { 4 }$. Select the correct options. (1) $a _ { 2 } = 2$ (2) $b _ { 2 } = \frac { 3 } { 4 }$ (3) The sequence $< b _ { n } >$ is a geometric sequence with common ratio $\frac { 2 } { 3 }$ (4) For any positive integer $n$, $3 ^ { n } a _ { n }$ is always a positive integer (5) $b _ { 10 } < 10 ^ { - 4 }$
A sequence $< a _ { n } >$ satisfies $3 a _ { n + 1 } = a _ { n } + n$ (for all positive integers $n$) and $a _ { 1 } = 2$. Let the sequence $< b _ { n } >$ satisfy $b _ { n } = a _ { n } - \frac { n } { 2 } + \frac { 3 } { 4 }$. Select the correct options.\\
(1) $a _ { 2 } = 2$\\
(2) $b _ { 2 } = \frac { 3 } { 4 }$\\
(3) The sequence $< b _ { n } >$ is a geometric sequence with common ratio $\frac { 2 } { 3 }$\\
(4) For any positive integer $n$, $3 ^ { n } a _ { n }$ is always a positive integer\\
(5) $b _ { 10 } < 10 ^ { - 4 }$