# Problem of the Day: 2/3/13

Kira has a circular garden 20 feet in diameter. How many small shrubs, 6 inches in diameter, can she plant around the circumference of the circle as shown?

Solution to yesterday’s problem:

Notice that the 12th term and the 30th term are the same distance from the 21st term. So no matter how much is added to each successive term in the sequence, the 12th term will always be the same amount less than the 21st term as the 30th term is more. Since the 21st term is 47, let’s call the 12th term $47-n$ and the 30th term $47+n$. The sum of the 12th and 30th terms is $(47-n)+(47+n)$. The n‘s cancel out, leaving 47 + 47. So the sum of the 12th and 30th terms in the sequence is 94.