a. The seventh term of an arithmetic progression is 19 and the sum of the first twelve

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a. The seventh term of an arithmetic progression is 19 and the sum of the first twelve terms is 224.
Find the fourth term.
b. A geometric progression has first term 3 and common ratio r. A second geometric progression has first term 2 and common ratio 1/5r. The two progressions have the same sum to infinity, S. Find the value of r and the value of S.

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