a. The first term of a geometric progression in which all the terms are positive is 50.

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a. The first term of a geometric progression in which all the terms are positive is 50. The third term is 32.

Find the sum to infinity of the progression.

b. The first three terms of an arithmetic progression are 2sinx, 3cosx and (sinx + 2cosx) respectively, where x is an acute angle.

i. Show that tan x = 4/3.

ii. Find the sum of the first twenty terms of the progression.

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