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Question

Assertion :Between two numbers whose sum is 216, an even number of arithmetic means are inserted. If the sum of these means exceeds their number by unity, then the number of means are 12 Reason: If a and b are two given numbers and A1,A2,...,An are n arithmetic means between them, then A1+A2+...+An=n(a+b2)

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
If a and b are two numbers , and A1,A2,....An n means are inserted between them then, total sum of numbers =n+22(a+b)
Sum of the arithmatic means inserted will be =sum of the numbers - (a+b)
A1+A2+A3+....+An=n+22(a+b)(a+b)
=(a+b)×(n2)
Sum=n(a+b2) .......(1)
a+b=216=136
Sum=n+1
From (1), we have
n(a+b2)=n+1
13n12=n+1
13n=12n+12
n=12

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