ques related to arithmetic progression .
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Heya User,
[tex]S_n = \frac{n}{2} [ 2a + ( n - 1 )d ] = np ----- 2a + ( n - 1 )d = 2p ------- (i) \\\\ S_m = \frac{m}{2} [ 2a + ( m - 1 )d ] = m^{2} p ----- 2a + ( m - 1 )d = 2mp ------- (ii) \\ \\ S_m - S_n = ( m - n )d = ( m - 1 )2p \\ \\ n = 1 \ || \ d = 2p ----- [ Satisfies \ the \ Qn. ] \\ \\ a = p \ || \ d = 2p \\ \\ S_p = \frac{p}{2} [ 2p + ( p - 1 )2p ] = \frac{p}{2} [ 2p + 2 p^{2} - 2p ] = p^3[/tex]
And hence, we have S(p) = p³
^_^ We're done.. Hope it helps :)
[tex]S_n = \frac{n}{2} [ 2a + ( n - 1 )d ] = np ----- 2a + ( n - 1 )d = 2p ------- (i) \\\\ S_m = \frac{m}{2} [ 2a + ( m - 1 )d ] = m^{2} p ----- 2a + ( m - 1 )d = 2mp ------- (ii) \\ \\ S_m - S_n = ( m - n )d = ( m - 1 )2p \\ \\ n = 1 \ || \ d = 2p ----- [ Satisfies \ the \ Qn. ] \\ \\ a = p \ || \ d = 2p \\ \\ S_p = \frac{p}{2} [ 2p + ( p - 1 )2p ] = \frac{p}{2} [ 2p + 2 p^{2} - 2p ] = p^3[/tex]
And hence, we have S(p) = p³
^_^ We're done.. Hope it helps :)
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