The eighth and tenth terms of a sequence are 64 and 100 if the sequence is either arithmetic or geometric the ninth term can not be

(1) -82
   In an arithmetic sequence, the common difference can be found be subtracting the 8th term from the 10th term and dividing by 2 (which is 10 - 8). If we do that, we get (100-64)/2, which is 18. 64 + 18 = 82, which eliminates choice (4). (At this point, you might suspect that -82 is likely the answer.) In a geometric sequence, the common ratio can be found by dividing the 10th term by the 8th term and then taking the square root (because the ratio is applied twice to get from the 8th term to the 10th term). So (100/64)^.5 = +1.25, which are the common ratios. It is important to remember that the square root may positive or negative. Then 64 * 1.25 = 80, and 80 * 1.25 = 100 And 64 * (-1.25) = -80 and -80 * 1.25 = 100. This eliminates choices (2) and (3).

What’s the improper fraction?