Question

What are common mistakes students make with geometric sequences?

Answer 1

One common error is not correctly finding the value of r, the common multiplier.

For example, for the geometric sequence `1/4, 1/2, 1, 2, 4, 8, ...` the multiplier r = 2. Sometimes the fractions confuse students.

A more difficult problem is this one: `-1/4, 3/16, -9/64, 27/56, ...` . 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: `(second term)/(first term)` which is `(3/16)/(-1/4)=3/16*-4/1=-3/4`. Thus the common multiplier is r = `-3/4`.
Also, you might check that this is consistently true by multiplying your constant multiplier by some other term (such as the third term) to see if you get the 4th term as the answer. This will help you verify that the sequence is indeed a geometric one.