Missing Term

Find the missing term in the series 0, 4, 18, 48, __, 180.

58 68 100 84

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2 solutions

Ossama Ismail
Jan 1, 2015

0 × 0 = 0 1 × 4 = 4 2 × 9 = 18 3 × 16 = 48 4 × 25 = 100 5 × 36 = 180 general term = ( n 1 ) × n 2 \begin{aligned} 0 \times 0 &= 0 \\ 1 \times 4 &= 4 \\ 2 \times 9 &= 18 \\ 3 \times 16 &= 48 \\ 4 \times 25 &= 100 \\ 5 \times 36 & = 180 \\ \cdots & \cdots \\ \text{general term} &= (n-1) \times n^2 \end{aligned}

Nelson Mandela
Jan 1, 2015

so the series is 0,4,18,48,?,180.......................................(1)

the difference between the terms are 4,14,30.........(2)

the difference between these terms are 10,16........(3)

so the next term in series 3 would be 16+6=22.

that means the next term in series 2 would be 30+22=52.

that means the next term in series 1 would be 48+52=100.

try to construct a pyramid to make things easier. you can also verify and find out that the next term is 180.

T n = ( n 1 ) ( n 2 ) T_n=(n-1)(n^2)

Satvik Golechha - 6 years, 5 months ago

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Thanks for the clarification.

Nelson Mandela - 6 years, 5 months ago

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