Question

Suppose Karl puts one penny in a jar, the next day he puts in three pennies, and the next day he puts in nine pennies. If each subsequent day Karl were able to put in three times as many pennies, how many pennies would he put in the jar on the 10th day?

Answer 1

19,683

Explanation:

You want the 10th term of a geometric sequence with first term 1 and a common ratio of 3.

Geometric sequence

The n-th term of a geometric sequence with first term a1 and common ratio r is ...

an = a1·r^(n-1)

For a1=1 and r=3, the 10th term is ...

a10 = 1·3^(10-1) = 3^9 = 19,683

Karl would put 19,683 pennies in the jar on the 10th day.

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Additional comment

On the 24th day, Karl would be putting into the jar the last of the 288 billion pennies in circulation.

The volume of added pennies on the 10th day is more than 7 liters, bringing the total that day to more than 10 liters. That's a pretty big jar.