Answer
False statement
Work Step by Step
Sequence $10,15,20,\ldots $
The general term or ${{n}^{th}}$ term of the arithmetic sequence is ${{a}_{n}}$.
and ${{a}_{n}}={{a}_{1}}+\left( n-1 \right)d$
Where, ${{a}_{1}}$ is the first term and $d$ is the difference between the consecutive terms (common difference).
Here ${{a}_{1}}=10$
And $d={{a}_{n+1}}-{{a}_{n}}$
$\begin{align}
& d={{a}_{n+1}}-{{a}_{n}} \\
& ={{a}_{1+1}}-{{a}_{1}} \\
& ={{a}_{2}}-{{a}_{1}}
\end{align}$
Put ${{a}_{1}}=10$ and ${{a}_{2}}=15$
$\begin{align}
& d={{a}_{2}}-{{a}_{1}} \\
& =15-10 \\
& =5
\end{align}$
Next term of the given sequence $10,15,20,\ldots $is ${{4}^{th}}$ term
$\begin{align}
& {{a}_{4}}={{a}_{1}}+\left( 4-1 \right)d \\
& =10+3\times 5 \\
& =10+15 \\
& =25
\end{align}$
Thus, the next term in the arithmetic sequence $10,15,20,\ldots $ is 25.
Therefore, the given statement ‘The next term in the arithmetic sequence $10,15,20,\ldots $ is 35’ is false.
