InterviewSolution
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InterviewSolution
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The first term of an A.P. is `a`and the sum of first `p`terms is zero, show tht the sum of its next `q`terms is `(a(p+q)q)/(p-1)dot` |
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Answer» Let the common difference of the given AP be d. then , ` S_(p) = 0 Rightarrow p/2 xx [ 2a + + ( p-1) d] =0` ` Rightarrow 2a + ( p-1) d=0 Rigtharrow = ( -2a)/( (p-1))` ` S_(p+q) + (( p+q))/2 .[ 2a + ( p+q-1) d]` `= (( p+q))/ 2[ ( 2a + ( p+q-1)xx ((-2a))/((p -1))]` ` =a ( p+q) .[ 1-((p+q -1))/((p-1))] = (-a(=+q)q)/((p-1))` Hence, the requird sum is ` (-a (p+q)q) / (( p-1))` |
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