How many cards would be needed for a 65 storey house of cards if there was 3 on the top row with it increasing by 3 each time you go down on

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How many cards would be needed for a 65 storey house of cards if there was 3 on the top row with it increasing by 3 each time you go down on

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How many cards would be needed for a 65 storey house of cards if there was 3 on the top row with the number of cards on each storey increasing by 3 each time you go down one storey. Example: One storey of cards has 3 cards, 2 storeys have 9 cards and so on so forth

Guest May 1, 2014

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Note that we are summing 3(1) + 3(2) + 3(3) + ....+ 3(64) + 3(65)

Another way to see this is that the sum of the 1 ^st 65 positive integers = [(65)(66) / 2] = 2145

So we have 3 * (1 + 2 + 3 + .... + 64 + 65) = 3 * [(65)(66) / 2] = 6435

CPhill May 1, 2014

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CPhill · Answer 1 · 2014-05-01T05:26:57

Note that we are summing 3(1) + 3(2) + 3(3) + ....+ 3(64) + 3(65)

Another way to see this is that the sum of the 1 ^st 65 positive integers = [(65)(66) / 2] = 2145

So we have 3 * (1 + 2 + 3 + .... + 64 + 65) = 3 * [(65)(66) / 2] = 6435

Guest · Answer 2 · 2014-05-01T05:02:00

well by the formula you provided it would be 3 raised to the 65th power which is $${{\mathtt{3}}}^{{\mathtt{65}}} = {\mathtt{10\,301\,051\,460\,877\,537\,453\,973\,547\,267\,843}}$$ cards.

How many cards would be needed for a 65 storey house of cards if there was 3 on the top row with it increasing by 3 each time you go down on

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