# ntresting problem

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#1

Ive been trying to work it out but i need help
0
15 years ago
#2
You can use this

Code:
```level	Num cards
1	2 + 1
2	4 + 2
3	6 + 3
.
.
n	2n + n```
Let Sn be number of cards to build n storeys

S1 = 3
S2 = S1 + 6
S3 = S2 + 9 = S1 + 6 + 9 = 3 + 6 + 9 = 3(1 + 2 + 3)
.
.
Sn = 3(1 + 2 + 3 + ... + n) Sigma ( 1 + 2 + 3 + ... + n ) = n/2(n+1)
Sn = (3n/2)(n+1)
============

Edit: I've just noticed, looking at the picture, there are no cards on the very bottom of the house. The formula would have to be modified for this
0
#3
what can i say the nth term is
0
15 years ago
#4
(Original post by mafakuza)
what can i say the nth term is
The nth term ?

Do you mean the nth term as in the number of cards in the nth layer (or storey) of the house?
Or, the nth term as in the overall number of cards to build n layers (or storeys) of the house?

Sn = (3n/2)(n+1)

The nth storey has n cards on it's bottom-most layer, so the modified version of Sn is,

Sn = (3n/2)(n+1) - n
================

If house is 10 storeys high then n=10.

S10 = (3*10/2)(10 + 1) - 10
S10 = 15*11 - 10
S10 = 155
========

For a 62-storey high house, n = 62.

S62 = (3*62/2)(62 + 1) - 62
S62 = 93*63 - 62
S62 = 5089 - 62
S62 = 5797
=========
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