
Kazuhiko O. answered 06/07/21
Compassionate Math Tutor
Another way you can think about this is by thinking about what it means to be a geometric sequence. In a geometric sequence, you get the next term by multiplying the previous number by some constant x. So, for a sequence a, b, c, b = xa and c = xb.
This means that x should equal b/a as well as c/b and you can set those equal to each other and simplify to get b^2=ac. This gets you to the same equation that Mark had above with n+1=a, n+9*=b, n+25=c
(*Mark had n+6, but the second term, n+3, is increased by 6 making it n+3+6=n+9)