2014 AMC 12A Problem 9

Problem 9 of 25EasierAlgebra

Five positive consecutive integers starting with

a

have average

b.

What is the average of

5

consecutive integers that start with

b?

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Solution

The integers

a,a+1,a+2,a+3,a+4

have average

a+2,

b=a+2.

The integers starting at

b

have average

b+2=(a+2)+2=a+4.

Thus, the correct answer is B.

Concepts: mean · arithmetic sequence

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.