[" If "a(m)" be the "m" th term of an A....

[" If "a_(m)" be the "m" th term of an A.P.,then "],[a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+...+a_(2n-1)^(2)-a_(2n)^(2)=],[[" A."(n-1)/(2n-1)(a_(1)^(2)-a_(2n)^(2))," B."(n)/(2n-1)(a_(2n)^(2)-a_(1)^(2))],[" C."quad (n)/(2n-1)(a_(1)^(2)-a_(2n)^(2))," D.None of these "]]

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If a_(m) be the mth term of an AP, show that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+"...."+a_(2n-1)^(2)-a_(2n)^(2)=(n)/((2n-1))(a_(1)^(2)-a_(2n)^(2)) .

If the sequence a_(1),a_(2),a_(3),…,a_(n) is an A.P., then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+…+a_(2n-1)^(2)-a_(2n)^(2)=n/(2n-1)(a_(1)^(2)-a_(2n)^(2))

Let the sequence a_(1),a_(2),a_(3),...,a_(n) from an A.P.Then the value of a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-...+a_(2n-1)^(2)-a_(2n)^(2) is (2n)/(n-1)(a_(2n)^(2)-a_(1)^(2))(b)(n)/(2n-1)(a_(1)^(2)-a_(2n)^(2))(n)/(n+1)(a_(1)^(2)-a_(2n)^(2))(d)(n)/(n-1)(a_(1)^(2)+a_(2n)^(2))

If the sequence a_(1),a_(2),a_(3),dots a_(n),.... forms an A.P.then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)+...+a_(4)^(2)=(n)/(2n-1)(a_(1)^(2)-a_(2n)^(2))

If a_(1),a_(2),a_(3)"....." are in GP with first term a and common ratio r, then (a_(1)a_(2))/(a_(1)^(2)-a_(2)^(2))+(a_(2)a_(3))/(a_(2)^(2)-a_(3)^(2))+(a_(3)a_(4))/(a_(3)^(2)-a_(4)^(2))+"....."+(a_(n-1)a_(n))/(a_(n-1)^(2)-a_(n)^(2)) is equal to

If a_(1),a_(2),a_(3)"....." are in GP with first term a and common rario r, then (a_(1)a_(2))/(a_(1)^(2)-a_(2)^(2))+(a_(2)a_(3))/(a_(2)^(2)-a_(3)^(2))+(a_(3)a_(4))/(a_(3)^(2)-a_(4)^(2))+"....."+(a_(n-1)a_(n))/(a_(n-1)^(2)-a_(n)^(2)) is equal to

[" If "a_(m)" be the "m" th term of an A.P.,then "],[a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+...+a_(2n-1)^(2)-a_(2n)^(2)=],[[" A."(n-1)/(2n-1)(a_(1)^(2)-a_(2n)^(2))," B."(n)/(2n-1)(a_(2n)^(2)-a_(1)^(2))],[" C."quad (n)/(2n-1)(a_(1)^(2)-a_(2n)^(2))," D.None of these "]]

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