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Geometric Sequencesmedium
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An infinite geometric series has a common ratio rrr such that ∣r∣<1|r| < 1∣r∣<1. The sum of the odd-indexed terms (a1+a3+a5+…a_1 + a_3 + a_5 + \dotsa1​+a3​+a5​+…) is 999, and the sum of the even-indexed terms (a2+a4+a6+…a_2 + a_4 + a_6 + \dotsa2​+a4​+a6​+…) is 333. What are the values of the first term a1a_1a1​ and the common ratio rrr?