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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Question : The average of $n$ numbers is $a$. The first number is increased by 2, the second one is increased by 4, the third one is increased by 8, and so on. The average of the new numbers is:
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