Hooray for Number Patterns!

Level 1

Find the 12th term in the pattern of real numbers.

2 3 , 1 1 5 , 1 5 7 , 2 2 9 , 2 8 11 , ⋯ \frac{2}{3}, 1 \frac{1}{5}, 1 \frac{5}{7}, 2 \frac{2}{9}, 2 \frac{8}{11}, \cdots

5 4 19 5 \frac{4}{19} 6 17 36 6 \frac{17}{36} 6 6 25 6 \frac{6}{25} 5 9 49 5 \frac{9}{49}

Jeremy Bansil by Jeremy Bansil , 27, Philippines

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4 solutions

Mihir Chakravarti
Dec 13, 2014

The quickest way to solve this was by observing that the denominator of the terms are in A P AP with common difference 2 and first term 3 so, by using the formula T n = a + ( n − 1 ) d T_{n} = a + (n-1)d we get the 12th term as 25 and the only answer having 25 in its denominator was the second option.

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Anna Anant
Dec 24, 2014

2/3 , 6/5 , 12/7 , 20/9 , 30/11

T(1)=2/3 T(n)=(n^2-1)+(n-1)+2/2n+1

T(12)=(144-1)+(12-1)+2/(2*12)+1=156/25 or 6 6/25

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Rishy Fishy
Dec 23, 2014

the numerator is n^2 +n (144+12)

The denominator is 2n+1 (24+1)

So the answer is 156/25

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Ahmed Ezz
Dec 23, 2014

denominator is arithmetic sequence = 2*n +1 numerator general term = n^2 + n

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