Question : The average of five consecutive positive integers is n. If the next two integers are also included, the average of all these integers will:
Option 1: increase by 1.5
Option 2: increase by 1
Option 3: remain the same
Option 4: increase by 2
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Correct Answer: increase by 1
Solution :
Let $(x–2),(x–1), x, (x+1), (x+2)$ be the 5 consecutive positive integers.
The average of an AP with an odd number of terms = middle term
$⇒ x = n$
When the next two integers are also included,
$⇒ (x–2),(x–1), x, (x+1), (x+2), (x+3), (x+4)$
New average = middle term $= (x+1) = n+1$
⇒ Average has increased by 1.
Hence, the correct answer is 1.
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