Name: David Grimmer
Who is asking: Student
Level: Middle

Question:
Complete the following sequence so that, after the first two terms, each successive term is the average of all the preceding terms.

20__ __ 28 __ __

Suppose that the sequence starts 20 x y 28 then you know two facts,

• y is the average of 20 and x.
• 28 is the average of 20, x and y.

From the second of these 28 = (20 + x + y)/3 so 84 = 20 + x + y and hence x + y = 64. Thus y = 64 - x.

Now the first fact can be stated, 64 - x is the average of 20 and x. Can you finish it?