an aritmetic sequence is like this
[tex]a_n=a_1+d(n-1)[/tex] where a1=first term and d=common difference
geometric is [tex]a_n=a_1(r)^{n-1}[/tex] 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 [tex]d(n-1)=(r)^{n-1}[/tex]
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
