Geometric Sequenceshard
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Suppose a1,a2,a3a_1, a_2, a_3 is a geometric sequence of positive integers with common ratio r>1r > 1. Let b1,b2,b3b_1, b_2, b_3 be an arithmetic sequence. If a1=b1a_1 = b_1, a2=b2+2a_2 = b_2 + 2, and a3=b3+8a_3 = b_3 + 8, and the common difference of the arithmetic sequence is a positive integer, which of the following are possible values for the first term a1a_1 and the common ratio rr?