Question

Suppose you received a penny on the first day of

December, two pennies on the second day of December,
four pennies on the third day, eight pennies on the
fourth day and so on. How many pennies would you
receive on December 31 if this pattern continues?

Answer 1

Explanation:

Number of pennies received in the month of December are given as:

1, 2, 4, 8, 16,........

which is in Geometric Progression.

here, first term a = 1

`common \: ratio \: r = (2)/(1) = 2 \\ \\ \because \: S_n = \frac{a( {r}^(n) - 1)}{r-1} \\\\</p><p>\therefore \: S_(31)= \frac{1* ( {2}^(31) - 1)}{2-1} \\\\</p><p>\therefore \: S_(31)= ( (2147483648 - 1))/(1) \\\\</p><p>\therefore \: S_(31)= ( 2147483647)/(1) \\\\</p><p>\therefore \: S_(31)=2147483647`

So, on 31st of December he will have 2147483647 pennies.