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Question:

If the sum of the first 15 terms of the series 34/3 + 112/3 + 214/3 + 33 + 334/3 +...........is equal to 225k. then k is equal to:

9

27

54

108

Solution:

⟮34⟯3+⟮64⟯3+⟮94⟯3+⟮124⟯3+..15termS=15∑r=1[3r4]3=2764∑r3=276415∑r=1r3=2764.[15(15+1)2]2=27×225(given in question)K=27