Determine whether a series is arithmetic or geometric

Question

Whether the following sequence is arithmetic or geometric $7, 7, 7, 7,\ldots$ I think it satisfies both conditions of arithmetic and geometric sequences but if we try to calculate the sum of finite terms of it using the geometric series sum we get $$S_n=\frac{7 \cdot 0}{0}$$ which is indeterminate but it is okay with the arithmetic series then it is arithmetic sequence . Does that correct or not ?

Answer 1

You should verify things from definition.

As you said, it satisfy both conditions hence it is both an arithmetic sequence and a geometric sequence.

The formula that you used required us to check the condition of the common ratio is not one.

If the common ratio is $1$, then $S_n = a_0n$.