Which two numbers will follow the given pattern- 1 nbsp- 2 nbsp- 1 nbsp- 2 nbsp- 1 nbsp- - nbsp- -1 nbsp- 12 nbsp- 21 nbsp- 22 nbsp- 1

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Pattern Identification

Which two num...

Question

Which two numbers will follow the given pattern?
1 2 1 2 1 _ _

1 1

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2 2

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1 2

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2 1

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Solution

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1^{2} = \frac{1}{6} [1 \times (1 + 1) \times (2 \times 1 + 1)] 1^{2} + 2^{2} = \frac{1}{6} [2 \times (2 + 1) \times (2 \times 2 + 1)] 1^{2} + 2^{2} + 3^{2} = \frac{1}{6} [3 \times (3 + 1) \times (2 \times 3 + 1)] 1^{2} + 2^{2} + 3^{2} + 4^{2} = \frac{1}{6} [4 \times (4 + 1) \times (2 \times 4 + 1)]

\frac{G_{1}^{2}}{G_{2}} + \frac{G_{2}^{2}}{G_{1}} = 2 A

1 = \frac{1}{2} (1 \times (1 + 1))

1 + 2 = \frac{1}{2} (2 \times (2 + 1))

1 + 2 + 3 = \frac{1}{2} (3 \times (3 + 1))

1 + 2 + 3 + 4 = \frac{1}{2} (4 \times (4 + 1))

31 + 32 + . . . + 50

1 = \frac{1}{2} (1 \times (1 + 1))

1 + 2 = \frac{1}{2} (2 \times (2 + 1))

1 + 2 + 3 = \frac{1}{2} (3 \times (3 + 1))

1 + 2 + 3 + 4 = \frac{1}{2} (4 \times (4 + 1))

1 + 2 + 3 + 4 + 5 + . . . . + 50

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