The average of 5 consecutive integers is n. If the next two consecutive integers are also included, what will be the new average of all 7 integers?

Introduction:
Averages of consecutive integers track the middle value. For an odd count, the average equals the exact middle term. Adding two next higher consecutive numbers shifts the middle position upward by one, thus increasing the average by exactly 1, irrespective of n.

Given Data / Assumptions:

• Five consecutive integers centered at some integer m
• Average of these five = n, so m = n
• Add the next two consecutive integers (m + 3 and m + 4)

Concept / Approach:
For 5 numbers, the middle is the 3rd term = m = n. For 7 numbers, the middle is the 4th term, which is m + 1. Hence the average increases by exactly 1. No computation of actual values is necessary beyond understanding the symmetry of consecutive integers.

Step-by-Step Solution:

Verification / Alternative check:
Test with m = 10: original average of 8, 9, 10, 11, 12 is 10. Adding 13 and 14, the 7-number average is 11. Increase = 1.

Why Other Options Are Wrong:
Increases by 2 or 1.4 contradict the fixed shift of the middle; “Remains the same” is false; “Decrease by 1” is impossible when only larger values are added symmetrically above.

Common Pitfalls:
Averaging endpoints or miscounting positions; always use the middle term logic for consecutive sequences.

Final Answer:
increase by 1