The first, fifth and seventh terms of an Arithmetic Progression (AP) correspond to the first three consecutive terms of a decreasing Geometric Progression (G.P).
The first term of each progression is 64, the common difference of the AP is d and the common ratio of the G.P is r.
(a) (i) Write two equations involving d and r.
(ii) Find the values of d and r.
(b) Find the sum of the first 10 terms of:
(i) The Arithmetic Progression (A.P);
(ii) The Geometric Progression (G.P).
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