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.
• B. 12
• C. 12 x (first term)
• D. 24

Answer 1

The correct option is B

12

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

$a_n$ = $a_1$ + (n - 1)d

$\Rightarrow$ $a_n$ - $a_1$ = (n - 1)d

$\Rightarrow$ $\frac{a_n-a_1}{n-1}$ = 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.