Answer
False statement
Work Step by Step
${{a}_{n}}=3n-1$.
To find the value of $a{}_{17}$ put $n=17$ in the equation ${{a}_{n}}=3n-1$
$\begin{align}
& {{a}_{n}}=3n-1 \\
& {{a}_{17}}=\left( 3\times 17 \right)-1 \\
& =51-1 \\
& =50
\end{align}$
Thus, if ${{a}_{n}}=3n-1$ then ${{a}_{17}}=50$ not 19.
Therefore, the given statement “if ${{a}_{n}}=3n-1$ then ${{a}_{17}}=19$” is false.
