Help with Maths Assignment?

Question

I have an investigation to do.

I haveto found out how many cards in a 62 storey house of cards.

I know that 1 storey has 2 cards

2 storeys has 7

3 storeys has 15

4 storeys has 26

5 storeys has 40

6 storeys has 57

7 storeys has 77

8 storeys has 100

9 storeys has 126

10 storeys has 155

and now i haveto find a rule to find out the 62 storey.

Can anyone figure out the rule and if you can tell mehow you got it?

Answer 1

the card house consists of pairs of cards supporting each other and on each floor there's a base for the next floor.

the formula for the pairs is (n+1)n

the formula for the base is n(n-1)/2

their sum is your answer, n(n+1+n/2-1/2)=1.5n^2+0.5n

that's the formula for an arithmetic series, Sn=(a1+an)n/2

both the pairs and the base are arithmetical series but for the base

n is n-1 because you don't need a base for the first flore.

if n=62 the sum=1.5*62^2+0.5*62=5766+31=5797

Answer 2

try this formula

if n is the number of storeys

then

no of cards is=[ (1+2+.......+n)x3] - n

ie if number of storeys n= 4

no of cards= [(1+2+3+4)x3]-4= (10X3) - 4 = 26

now u can find the answer  

i think the answer is 5797. please verify it with a calculator.