Sam is collecting marbles. He collects 3 on the first day, 7 marbles on the second day, 15 marbles on the third day, 31 on the fourth day, and 63 marbles on the fifth day. If this pattern continues, the number of marbles Sam will collect on the sixth day is __________

The correct answer is: 127

Step by step solution:
number of marbles Sam collected on the first day = 3 
number of marbles Sam collected on the second day = 7 = 3 + 2 x 2
number of marbles Sam collected on the third day = 15 = 7 + 2 x 2 x 2
number of marbles Sam collected on the fourth day = 31 = 15 + 2 x 2 x 2 x 2
number of marbles Sam collected on the fifth day = 63 = 31 + 2 x 2 x 2 x 2 x2 
Thus, the rule is as follows:
number of marbles collected by Sam on nth day = number of marbles calculated  by Sam on (n-1)th day + 2 x 2 x 2...( n times)
Thus, number of marbles Sam collected on the sixth day = number of marbles Sam collected on the fifth day + 2 x 2 x 2 x 2 x 2 x 2
= 63 + 64
= 127
Thus, Sam collected 127 marbles on the sixth day.
Hence, option(b) is the correct option.