If `a_1,a_2, a_3……….` are in H.P. and `f(k) =sum_(r=1)^n a_r-a_k, the a_1/(f(1)), a_2/(f(2))

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If `a_1,a_2,a_3……..a_n` are in H.P. and `f(k) = sum_(r=1)^na_r-a_k` then ` (f(1))/a_1, (f(2))

If `a_1, a_2, a_3,.....a_n` are in H.P. and `a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1

If `a_1, a_2, a_3,.....a_n` are in H.P. and `a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1

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Let \[{a_1},{a_2},{a_3},........\] be in an A.P. such that \[\sum\limits_{k = 1}^{12} {{a_{2k - 1}}}