Can a sequence be both arithmetic and geometric?

An aritmetic sequence is like this
where a1=first term and d=common difference

geometric is where a1=first term and r=common ratio

can it be both aritmetic and geometric
hmm, that means that the starting terms should be the same

therfor we need to solve
what values of d and r make all natural numbers of n true?
are there values that make all natural numbers for n true?

when n=1, then d(1-1)=0 and r^(1-1)=1, so already they are not equal

the answer is no, a sequence cannot be both aritmetic and geometric