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