If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first for term

Answer Details

Let us denote the first term of the G.P. by a and the common ratio by r. Then the 2nd term is ar, the 3rd term is ar^2, and so on. Therefore, the 5th term is ar^4.
We have two pieces of information, namely that ar = 6 and ar^4 = 48. Dividing the second equation by the first, we obtain (ar^4)/(ar) = r^3 = 48/6 = 8. Therefore, r = 2.
Using this value of r, we can solve for a by using the equation ar = 6. Substituting r = 2, we obtain 2a = 6, so a = 3.
Therefore, the first four terms of the G.P. are 3, 6, 12, 24, and their sum is 45. Thus, the correct answer is 45.