MATHEMATICS

JAMB 2004 - Question 19

Mathematics 2004 JAMB Past Questions - Question 19: Given that the first and fourth terms of a GP are 6 and 162 respectively ,find the sum of the three terms of the progression

Given that the first and fourth terms of a GP are 6 and 162 respectively ,find the sum of the three terms of the progression
A:
B:
C:
D:
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Correct Answer

D

Explanation

To find the sum of the three terms of a geometric progression (GP), we need to determine the common ratio (r) and then calculate the sum using the formula.Given that the first term (a₁) is 6 and the fourth term (a₄) is 162, we can use these values to find the common ratio.a₁ = 6a₄ = 162We know that the nth term of a GP can be calculated using the formula:aₙ = a₁ * r^(n-1)Substituting the values for a₁ and a₄, we have:6 * r^(4-1) = 162Simplifying the equation:6 * r^3 = 162Dividing both sides by 6:r^3 = 27Taking the cube root of both sides:r = 3Now that we have the common ratio (r = 3), we can calculate the sum of the three terms using the formula:Sum = a₁ + a₂ + a₃Substituting the values for a₁ and r, we have:Sum = 6 + 6 * 3 + 6 * 3^2Simplifying:Sum = 6 + 18 + 54Sum = 78Therefore, the sum of the three terms of the geometric progression is 78.