Question

the common difference of an Ap in which a15- a6,=-27/2 is

Answer 1

-27/16 is the correct answer

Answer 2

Answer: The common difference of the AP is $-\frac{3}{2}$.

Explanation:

The $n_{th}$ term of an AP is defined by,

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

Where, a is the first term and d is the common difference.

First we find $a_{15}$.

$a_{15}=a+(15-1)d$

$a_{15}=a+14d$

Now, find the value of  $a_6$.

$a_6=a+(6-1)d$

$a_6=a+5d$

The given equation is,

$a_{15}-a_6=-\frac{27}{2}$

$a+14d-a-5d=-\frac{27}{2}$

$9d=-\frac{27}{2}$

Divide both sides by 9.

$d=-\frac{3}{2}$

Therefore, the common difference of the AP is $-\frac{3}{2}$.