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.

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12 x (first term)

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Solution

The correct option is B
12

Let $a_{1}$ , be the first term, number of terms, common difference.

$a_{n}$ = $a_{1}$ + (n - 1)d

$\Rightarrow$ $a_{n}$ - $a_{1}$ = (n - 1)d

Dividing by $(n - 1)$

$\Rightarrow$ $\frac{a_{n} - a_{1}}{n - 1}$ = d which is the quotient and is equal to 12

$∴ d = 12$

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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.

The correct option is B 12 Let a1, be the first term, number of terms, common difference. an = a1 + (n - 1)d ⇒ an - a1 = (n - 1)d Dividing by (n−1) ⇒ an−a1n−1 = d which is the quotient and is equal to 12 ∴d=12

The correct option is B
12

Let $a_{1}$ , be the first term, number of terms, common difference.

$a_{n}$ = $a_{1}$ + (n - 1)d

$\Rightarrow$ $a_{n}$ - $a_{1}$ = (n - 1)d

Dividing by $(n - 1)$

$\Rightarrow$ $\frac{a_{n} - a_{1}}{n - 1}$ = d which is the quotient and is equal to 12

$∴ d = 12$