Geometric sequences

Here are two exercises about geometric sequences. Click here for a lesson about geometric sequences.

 

Question 1:

When sage Sissa created the chess game for his king, the sovereign decided to give Sissa whatever he wanted to reward him. Sissa then told his king:

«I'd like that you put one grain of wheat on the 1^st square of the chessboard, 2 ones on the 2^nd square, 4 ones on the 3^rd square, etc. until ye reach the last square, doubling the number of grains of wheat you put on the case each time.»

 

What number of grains of wheat did Sissa ask to the king? (N.B.: There are 64 squares on a chessboard.)

 

Question 2:

In a game, the player has to puts in a pot whatever amount of money he wants, then flip a coin; if he flip a head, the double of the money in the pot is added (for example, if the pot contain $1 and the coin land on a head, the double of $1, which is $2 will be added, and there will be $1+$2=$3 in the pot) and the player flips the coin again; if he flip a tail, he gets whatever's in the pot and the game ends.

 

The player bets $5 at the beginning of the game. What amount of money will he get if he flip:

• 1 tail?
• 2 tails?
• 5 tails?
• 10 tails?
• 666 tails?