The average of 5 consecutive integers starting with m is n. What is the…

To determine the average of 6 consecutive integers starting with (m + 2), let's break down the problem systematically.

Step-by-Step Analysis
Analyze the first sequence:

The 5 consecutive integers starting with m are: m, (m + 1), (m + 2), (m + 3), (m + 4).

The average of these integers is the middle term, which is (m + 2).

Given that this average is n, we establish the relationship: n = m + 2.

Analyze the second sequence:

The 6 consecutive integers starting with (m + 2) are: (m + 2), (m + 3), (m + 4), (m + 5), (m + 6), (m + 7).

The sum of these 6 integers is: 6m + (2 + 3 + 4 + 5 + 6 + 7) = 6m + 27.

The average is the sum divided by the count: (6m + 27) / 6 = m + 4.5.

Express the new average in terms of n:

We know from Step 1 that m = n - 2.

Substitute this into the average expression from Step 2: (n - 2) + 4.5 = n + 2.5.

Convert n + 2.5 into a fraction: (2n + 5) / 2.

Correct Option
Option A: (2n+5)/2