Let a is the first term and r is the common ratio of the GP.

Given S_n = P

=> P = a(rⁿ - 1)/(r - 1) .............1

and S_2n = 3P

=> 3P = a(r²ⁿ - 1)/(r - 1) .........2

From equation 1 and 2, we get

      3P/P = {a(r²ⁿ - 1)/(r - 1)}/{a(rⁿ - 1)/(r - 1)}

=> 3 = (r²ⁿ - 1)/(rⁿ - 1)

=> 3(rⁿ - 1) = (r²ⁿ - 1)

=> 3rⁿ - 3 = (r²ⁿ - 1)

=> r²ⁿ - 1 - 3rⁿ + 3 = 0

=> r²ⁿ - 3rⁿ + 2 = 0

=>  (rⁿ - 2)*(rⁿ - 1) = 0

=> rⁿ = 2, 1

Put rⁿ = 2 in equation 1, we get

      P = a(2 - 1)/(r - 1)

=> P = a/(r - 1) .............3

Now, S_3n = a(r³ⁿ - 1)/(r - 1)

=> S_3n = a(2³ - 1)/(r - 1)

=> S_3n = a(8 - 1)/(r - 1)

=> S_3n = 7a/(r - 1)

=> S_3n = 7P                  {from equation 3}

So, the sum of 1^st 3n terms of GP is 7P