For the $A . P . : - 3, - 7, - 11,,$ can we find $a_{30} - a_{20}$ without actually finding $a_{30}$ and $a_{20}$ ? Give reasons for your answer.

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Solution

$- 3, - 7, - 11, . . .$
it is an A,P with $a = - 3, d = - 4$
$a_{30} - a_{20}$
$= (a + 29 d) - (a + 19 d)$
$= a + 29 d - a - 19 d$
$= 10 d$
$= 10 \times - 4$
$= - 40$

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