If $\frac{\sqrt{2}}{3}$and $\frac{8\sqrt{2}}{81}$ be the 4^th and 10^th terms, respectively, of a geometric series, find the 7^th term of that series.

Serial numbers for a product are to be made using 2 letters followed by 3 numbers. If the letters are to be taken from the first 8 letters of the alphabet with no repetitions and the numbers are to be taken from the 10 digits (0-9) with no repetitions, how many serial numbers are possible?

On the same side of a tower two objects are located. The angles of depression of the two objects observed from the top of the tower are 30$°$ and 60$°$ If the height of the tower is $150\sqrt{3}$ m find the distance between the two objects.

A debt of Tk. 1000 with interest at 16%, compounded quarterly, is to be amortized by 20 quarterly equal payments over the next 5 years. What will be the amount of these payments?