What is the common difference of an A.P. in which $a_{24} - a_{17} = - 28$ ?

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Solution

General $n^{t h}$ term in AP, $a_{n} = a + (n - 1) d$
$a =$ first term, $d =$ common difference.
Given, $a_{24} - a_{17} = - 28$
$\Rightarrow (a + 23 d) - (a + 16 d) = - 28$
$\Rightarrow 23 d - 16 d = - 28$
$\Rightarrow 7 d = - 28$
$\Rightarrow d = - 4$ .

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