Answer
The statement:“I’ve noticed that the big difference between arithmetic and geometric sequences is that arithmetic sequences are based on addition and geometric sequences are based on multiplication”Makes sense
Work Step by Step
In Arithmetic Progression the series is represented by:
\[a,a+d,a+2d,a+3d,\ldots \]
It can be written as \[{{a}_{n}}=a+\left( n-1 \right)d\]
In this series,a denotes the first term and d denotes the common difference.
It can be say that arithmetic sequence based on addition sequences.
In Geometric Sequences, the series is represented by:
\[a,ar,a{{r}^{2}},a{{r}^{3}},\ldots \]
In this series, a denotes the first term and r denotes the common ratio
It can be written as \[{{a}_{n}}=a{{r}^{\left( n-1 \right)}}\]
It can be say that Geometric Sequences based on multiplication.
Thus,an arithmetic sequence and geometric sequence are the sequences in which arithmetic sequences are based on addition and geometric sequences are based on multiplication.
Hence, the provided statement makes sense.
