For the A.P. : $- 3, - 7, - 11, . . . . .,$ can we find $a_{30} - a_{20}$ withoput actually finding $a_{30} and a_{20}$ ? Give reasons for your answer.

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Solution

Consider the A.P −3, −7, −11, ....
$a = - 3, d = - 4, a_{30} - a_{20} = [a + (30 - 1) d] - [a + (20 - 1) d] a_{30} - a_{20} = a + 29 d - a - 19 d ∴ a_{30} - a_{20} = 10 d = 10 (- 4) = - 40$

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