Given that the first and forth terms of G.P are 6 and 162 respectively, find the sum of the first three terms of the progression

Given that the first and forth terms of G.P are 6 and 162 respectively, find the sum of the first three terms of the progression

Answer Details

To find the sum of the first three terms of a G.P, we need to determine the common ratio (r) of the progression. Given that the first and fourth terms are 6 and 162 respectively, we can use the formula for the nth term of a G.P to obtain: a1 = 6, a4 = 162 a4 = a1 * r^3 162 = 6 * r^3 r^3 = 27 r = 3 Now, we can find the second and third terms of the progression using the common ratio: a2 = a1 * r = 6 * 3 = 18 a3 = a2 * r = 18 * 3 = 54 The sum of the first three terms of the G.P is: a1 + a2 + a3 = 6 + 18 + 54 = 78 Therefore, the correct answer is option (C) 78.