Theory question 113
Progressions(a) The third term of a Geometric Progression (G.P) is 24 and its seventh term is 4 20/27. Find its first term.
(b) Given that y varies directly as x and inversely as the square of z. If y = 4, when x = 3 and z = 1, find y when x = 3 and z = 2.
Show the model answer
Model answer
(a) ar2 = 24 and ar6 = 128/27. Dividing: r4 = 128/648 = 16/81, so r = ±2/3.
a = 24 ÷ (4/9) = 54.
(b) y = kx/z2: 4 = 3k, so k = 4/3. When x = 3, z = 2: y = (4/3 × 3)/4 = 1.
Explanation
Divide the two term equations to remove a.