The sum of the first n …
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Sia ? 6 years, 4 months ago
Let the sum of first n terms of an A.P. is Sn, where first term i.e. a = 8 and the common difference i.e. d = 20.
and let the sum of first 2n terms of another A.P. is S'2n whose first term i.e. A= –30 and the common difference i.e. D = 8.
According to the question, Sn = S’2n
⇒ {tex}\frac { n } { 2 }{/tex} [2a + (n - 1)d] = {tex}\frac { 2 n } { 2 }{/tex} [2A + (2n - 1)D]
⇒ [2(8) + (n - 1)20] = 2[2(–30) + (2n - 1)8]
⇒ 16 + 20n - 20 = 2[-60 + 16n – 8]
⇒ 16 + 20n – 20 = 2[–68 + 16n]
⇒ 20n – 4 = –136 + 32n
⇒ –32n + 20n = –136 + 4
⇒ –12n = –132
⇒ n = {tex}\frac { 132 } { 12 }{/tex} = 11
Hence, the value of n is 11.
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