Answer
The provided statement is false.
Work Step by Step
The common difference for the arithmetic sequence provided by\[1,-1,-3,-5,\ldots \]is\[2\].
The common difference \[d={{a}_{2}}-{{a}_{1}}\]
It is provided that
\[\begin{align}
& {{a}_{1}}=1 \\
& {{a}_{2}}=-1
\end{align}\]
So,
\[\begin{align}
& d=-1-1 \\
& =-2
\end{align}\]
If the series will be \[1,3,5,7,9\ldots \], the common difference is \[2\].
Hence, the provided statement is false, if the series will be \[1,3,5,7,9\ldots \] then the common difference is\[2\].
