The average of 6 consecutive even numbers is 25. If the next even number is also considered, then what is the new average?

Let the first integer be 2x.

Average of 6 consecutive integers: (2x + (2x + 2) + ... + (2x + 10))/6= 12x + 2(1 + 2 + ... + 5) = 12x + 30 = 25 × 6 = 150

⇒ x = 10.

Average of new numbers: (2x + (2x + 2) + ... + (2x + 12) )/ 7 = (14x + 42)/7 = 2x + 6 = 20 + 6 = 26.