Find $a_{30} - a_{20} = - m$ for the A.P. $- 9, - 14, - 19, - 24, . . . . . . .$ . Find $m$ .

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Solution

Give A.P.- $- 9, - 14, - 19, . . . . . . . . . . . . . . . . . . .$
First term, $(a) = - 9$
Common difference, $(d) = a_{2} - a_{1} = - 14 - (- 9) = - 5$
As we know that,
$a_{n} = a + (n - 1) d$
$∴ a_{30} - a_{20} = (a + 29 d) - (a + 19 d)$
$\Rightarrow = a + 29 d - a - 19 d = 10 d = 10 \times - 5 = - 50$
Hence, the correct answer is 50.

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