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Consider the sequence of number [n+ 2 n + 1 2 ] for n 1 , where [x] denotes the greatest integer not exceeding x . If the missing integers in the sequence are n₁ < n₂ < n₃ < then find the n₁₂ .

Correct answer

78

Step-by-step solution

aligned & S_n=n+[ 2 n +0.5], n 1 & [ ]= G.I.F. aligned n 2 n [ 2 n +0.5] n+[ 2 n +0.5] 1 1.4 1 2 2 2 2 4 3 2.4 2 5 4 2.8 3 7 5 3.1 3 8 6 3.4 3 9 7 3.7 4 11 8 4 4 12 9 4.2 4 13 10 4.4 4 14 11 4.6 5 16 12 4.8 5 17 13 5..0 5 18 14 5.2 5 19 15 5.4 5 20 16 5.6 6 22 17 5.8 6 23 18 6 6 24 19 6.1 6 25 20 6.3 6 26 21 6.4 6 27 22 6.6 7 29 By observing pattern, 12^ th number in series =78

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