Question

If the common difference of an AP is -6, then find a16-a12​

Answer 1

$\sf\underline{Answer:}$

Given, in AP the common difference is -6

Common difference (d) = -6

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

$a_{16} = a + (16 - 1)( - 6)$

$a_{16} = a +(15)( - 6)$

$a_{16} = a - 90$

Let's find the 12th term of this AP

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

$a_{12} = a + (12 - 1)( - 6)$

$a_{12} = a + (11)( - 6)$

$a_{12} = a - 66$

$\sf\underline{Required~value:}$

$a_{16} - a_{12} = a - 90 - (a - 66)$

$= a - 90 - a + 66$

$\boxed{a_{16} - a_{12} = - 24}$

The required answer is -24

Have a good day!