Question

A radio company plans to create a new game show called Double Up. Contestants are asked a number of questions; they get £5 if they only answer one question correctly, £10 if they answer two questions correctly, £20 if they answer three questions correctly and so on. The money to be received doubles each time another question is answered correctly.
Which of the following options is the pay out for a contestant who correctly answers 20 questions?

Select one:

£52428800

£2621440

£100

£1310720

£200

£5242880

Answer 1

Answer:

The correct option is B) £2621440.

Step-by-step explanation:

Consider the provided information.

Contestants are asked a number of questions; they get £5 if they only answer one question correctly, £10 if they answer two questions correctly, £20 if they answer three questions correctly and so on.

This form a G.P

5, 10, 20, 40.....

The nth term of a GP series is $a_n=a_1\cdot r^{n-1}$

Where a₁ is the first term and r is the common ratio.

Here the first term is 5 and we need to find the value of 20th term.

The common ratio is: $\frac{a_2}{a_1}=\frac{10}{5}=2$

Substitute the respective values in the above formula.

$a_n=5\cdot 2^{20-1}$

$a_n=5\cdot 2^{19}$

$a_n=5\cdot 524288$

$a_n=2621440$

Hence, the correct option is B) £2621440.