If the sum of n terms of an AP is 3 - 4n, find, the common difference.

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Solution

Given,

$S_{n} = 3 - 4 n$

$S_{1} = 3 - 4 (1) = - 1 = a_{1}$

$S_{2} = 3 - 4 (2) = - 5$

$a_{2} = S_{2} - S_{1} = - 5 - (- 1) = - 4$

$∴$ common difference $d = a_{2} - a_{1} = - 4 + 1 = - 3$

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