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Question

There is a finite AP of n terms such that the difference between the last and first term when divided by (n-1), gives a quotient 12 and leaves no remainder. Find the common difference of this AP.


A

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B

12

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C

12 x (first term)

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D

24

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Solution

The correct option is B

12


If a1,n,d, be the first term, number of terms, common difference.

an = a1 + (n - 1)d

an - a1 = (n - 1)d

ana1n1 = d

Observe that the LHS is the ratio of the difference between the last and first term divided by (n-1), which is given in the problem. The quotient, which is 12, is in fact the common difference.

Hence the common difference of this AP is 12.


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