In a 'Make Ten' quiz game, contestants get \(\pounds 10\) for answering the first question correctly, then a further \(\pounds 20\) for the second question, then a further \(\pounds 30\) for the third, and so on, until they get a question wrong and are out of the game.
(A) Haroon answers six questions correctly. Show that he receives a total of \(\pounds 210\).
(B) State, in a simple form, a formula for the total amount received by a contestant who answers \(n\) questions correctly.
Hence find the value of \(n\) for a contestant who receives \(\pounds 10350\) from this game.
In a 'Double Your Money' quiz game, contestants get \(\pounds 5\) for answering the first question correctly, then a further \(\pounds 10\) for the second question, then a further \(\pounds 20\) for the third, and so on doubling the amount for each question until they get a question wrong and are out of the game.
(A) Gary received \(\pounds 75\) from the game. How many questions did he get right?
(B) Bethan answered 9 questions correctly. How much did she receive from the game?
(C) State a formula for the total amount received by a contestant who answers \(n\) questions correctly.
Hence find the value of \(n\) for a contestant in this game who receives \(\pounds 2621435\).