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
Question 1 Report
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.
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