The 3rd and 8th term of a GP are ⅓ and 81, respectively. Find the 2nd term.

Sure, here are the steps to solve the problem:

1. In a geometric progression (GP), the nth term is given by ar^(n-1), where a is the first term and r is the common ratio.

2. We know that the 3rd term is 1/3 and the 8th term is 81. So we can set up the following equations:

   ar^(3-1) = 1/3 ar^(8-1) = 81

3. Simplifying these equations gives us:

   ar^2 = 1/3 ar^7 = 81

4. We can divide the second equation by the first to eliminate a and solve for r:

   r^5 = (81)/(1/3) = 243 r = 3 (since 3^5 = 243)

5. Substituting r = 3 into the first equation gives us:

   a*3^2 = 1/3 a = (1/3)/(9) = 1/27

6. Now that we have a and r, we can find the 2nd term:

   a*r^(2-1) = (1/27)*3 = 1/9

So, the second term of the GP is 1/9.