If the sum of first 11 terms of an A.P., \( a_{1}, a_{2}, a_{3} \ldots \) is 0 \( \left(a_{1} \n...

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If the sum of first 11 terms of an A.P., \( a_{1}, a_{2}, a_{3} \ldots \) is 0 \( \left(a_{1} \neq 0\right) \), then the sum of the A.P., , \( a_{1}, a_{3}, a_{5} \ldots, a_{23} \) is math xmlns=http://www.w3.org/1998/Math/MathMLmik/mimsubmia/mimn1/mn/msub/math , where \( \mathrm{k} \) is equal to : 
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