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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, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 5 months ago

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

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CBSE > Class 09 > Mathematics