# Sequence

#### pkwiz

##### New member
We have 6 levels of cards - levels 1, 2, 3, 4, 5 and 6.

If 5 cards of one level = 2 of the next level
and 3 cards of one level = 1 of the next level ,
how many level 1 cards minimum would it take to get to a level 6 card?

#### Subhotosh Khan

##### Super Moderator
Staff member
We have 6 levels of cards - levels 1, 2, 3, 4, 5 and 6.

If 5 cards of one level = 2 of the next level
and 3 cards of one level = 1 of the next level ,
how many level 1 cards minimum would it take to get to a level 6 card?
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

#### pkwiz

##### New member
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

By my calculations it would take 125 level 1 cards minimum to get to level 6. I'm not sure if that's correct though so I would appreciate it if somebody double checks this.

#### AvgStudent

##### New member
I think you only need 98 level 1 cards to get level 6. Assuming the worse rate of 2.5cards of the previous level to get 1 of the next.
We can write a recursive formula:
$A_{n}=A_{n-1}\cdot\frac{2}{5}$

#### pkwiz

##### New member
I think you only need 98 level 1 cards to get level 6. Assuming the worse rate of 2.5cards of the previous level to get 1 of the next.
We can write a recursive formula:
$A_{n}=A_{n-1}\cdot\frac{2}{5}$
To get 1 six you would need 3 5's.

To get 3 5's you would need 8 4's (5 to get two and 3 to get 1 more).

To get 8 4's you would need 20 3's.

To get 20 3's you would need 50 2's.

To get 50 2's you would need 125 1's.

#### Cubist

##### Senior Member
To get 1 six you would need 3 5's.

To get 3 5's you would need 8 4's (5 to get two and 3 to get 1 more).

To get 8 4's you would need 20 3's.

To get 20 3's you would need 50 2's.

To get 50 2's you would need 125 1's.

I agree with your work, so well done, but I found your presentation a little hard to follow. I'd suggest that you write it like this:-
To get 1 on level 6 you would need 3 on level 5.
To get 3 on level 5 you would need 8 on level 4 (5 to get two and 3 to get 1 more).
To get 8 on level 4 you would need 20 on level 3.
To get 20 on level 3 you would need 50 on level 2.
To get 50 on level 2 you would need 125 on level 1.

Or even better:-
Code:
Level   number of cards
6           1
5           3
4           8
3          20
2          50
1         125