Sequence/Series question

[Guest]

Thoughtful Frank
-------------------

Thoughtful Frank has 100 movie tickets to give away to people at a local shopping centre. He gives the first person one ticket, the next person two tickets, the third person three tickets and so on until he can no longer give the nth person n tickets. How many tickets did the last lucky person receive? How many tickets did Frank have left?

My working out:

a = 1, d= 1(common difference)

Sn = n/2 (2a + (n-1)d)


100 = n + n^2
Using the quadratic formula, n = 13.65.

The answer is 13...I thought it would be 14...Any input?

thanks in advance

 

[stapel]

The question doesn't ask "how many people get any tickets at all?", but "how many people got the same number of tickets as their place in line?"

Could he give the fourteenth guy fourteen tickets?

Eliz.

 

[TchrWill]

Thoughtful Frank
-------------------

Thoughtful Frank has 100 movie tickets to give away to people at a local shopping centre. He gives the first person one ticket, the next person two tickets, the third person three tickets and so on until he can no longer give the nth person n tickets. How many tickets did the last lucky person receive? How many tickets did Frank have l

The sum of n consecutive is given by S = n(n + 1)/2

In this case, n(n _ 1).2 = 100 or n^2 + n - 200 = 0.

Solving, n =13.5 making the last numberot tnckets given out N = 13(14)/2 = 91 leaving him with 9 tickets.

So you were right.

 

[TchrWill]

Sorry for the typos:

Thoughtful Frank has 100 movie tickets to give away to people at a local shopping centre. He gives the first person one ticket, the next person two tickets, the third person three tickets and so on until he can no longer give the nth person n tickets. How many tickets did the last lucky person receive? How many tickets did Frank have l

The sum of n consecutive is given by S = n(n + 1)/2

In this case, n(n - 1)./.2 = 100 or n^2 + n - 200 = 0.

Solving, n =13.5 making the last numberot tnckets given out N = 13(14)/2 = 91 leaving him with 9 tickets.

So you were right.[/quote]