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If Sn denotes the sum of n terms of an AP whose common difference is d and 1st term is a. Find Sn – 2Sn – 1 + Sn – 2.

Posted by Technical 6G World 5 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 10 months ago

${\mathrm T}_\mathrm n\;=\;{\mathrm S}_\mathrm n\;-\;{\mathrm S}_{\mathrm n-1}$
${\mathrm T}_{\mathrm n-1}\;=\;{\mathrm S}_{\mathrm n-1}\;-\;{\mathrm S}_{\mathrm n-2}$
${\mathrm S}_\mathrm n\;-\;2{\mathrm S}_{\mathrm n-1}\;+\;{\mathrm S}_{\mathrm n-2}\;=\;{\mathrm S}_\mathrm n\;-\;{\mathrm S}_{\mathrm n-1}\;-\;{\mathrm S}_{\mathrm n-1}\;+\;{\mathrm S}_{\mathrm n-2}$
= $({\mathrm S}_\mathrm n\;-\;{\mathrm S}_{\mathrm n-1})\;-\;({\mathrm S}_{\mathrm n-1}\;-\;{\mathrm S}_{\mathrm n-2})$
= $({\mathrm T}_\mathrm n\;-\;{\mathrm T}_{\mathrm n-1})$
= d

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