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Find the 12th number in the sequence \(\frac{2}{3}, 1 \frac{1}{5}, 1 \frac{5}{7}, 2 \frac{2}{9}, 2 \frac{8}{11}, \cdots \)

 Jul 6, 2020
 #1
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so it becomes 2/3,6/5,12/7,20/9, so we have that the numerator is [number in sequence]^2+[number in sequence] and the denominator is 2*[number in sequence]+1 so we have that the 12th number in the sequence is ((12*12)+12)/(2*12+1)=(144+12)/25=156/25=6 6/25 so the 12th term is 156/25 or 6 6/25

 Jul 6, 2020

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