# What are common mistakes students make with geometric sequences?

For example, for the geometric sequence $\frac{1}{4} , \frac{1}{2} , 1 , 2 , 4 , 8 , \ldots$ the multiplier r = 2. Sometimes the fractions confuse students.
A more difficult problem is this one: $- \frac{1}{4} , \frac{3}{16} , - \frac{9}{64} , \frac{27}{56} , \ldots$ . It might not be obvious what the multiplier is, and the solution is to find the ratio of two successive terms in the sequence, as shown here: $\frac{\sec o n d t e r m}{f i r s t t e r m}$ which is $\frac{\frac{3}{16}}{- \frac{1}{4}} = \frac{3}{16} \cdot - \frac{4}{1} = - \frac{3}{4}$. Thus the common multiplier is r = $- \frac{3}{4}$.