I WANT TO ASK 2 QUESTIONS

Asked by parmodgulati | 6th Feb, 2014, 05:41: PM

Expert Answer:

Let S subscript P comma space S subscript Q comma S subscript R denotes the sum of P, Q and R terms of an A.P.
 
Given that, S subscript P equals A ; S subscript Q equals B ; S subscript R equals C
Thus, we have
 
S subscript P equals P over 2 open square brackets 2 a plus open parentheses P minus 1 close parentheses d close square brackets equals A S subscript Q equals Q over 2 open square brackets 2 a plus open parentheses Q minus 1 close parentheses d close square brackets equals B S subscript R equals R over 2 open square brackets 2 a plus open parentheses R minus 1 close parentheses d close square brackets equals C
 
Therefore, we have,
 
A over P equals 1 half open square brackets 2 a plus open parentheses P minus 1 close parentheses d close square brackets B over Q equals 1 half open square brackets 2 a plus open parentheses Q minus 1 close parentheses d close square brackets C over R equals 1 half open square brackets 2 a plus open parentheses R minus 1 close parentheses d close square brackets
 
Now consider the equation,
 
A over P open parentheses Q minus R close parentheses plus B over Q open parentheses R minus P close parentheses plus C over R open parentheses P minus Q close parentheses :
That is we have,
1 half open square brackets 2 a plus open parentheses P minus 1 close parentheses d close square brackets open parentheses Q minus R close parentheses plus 1 half open square brackets 2 a plus open parentheses Q minus 1 close parentheses d close square brackets open parentheses R minus P close parentheses plus 1 half open square brackets 2 a plus open parentheses R minus 1 close parentheses d close square brackets open parentheses P minus Q close parentheses equals a open parentheses Q minus R close parentheses plus b open parentheses R minus P close parentheses plus c open parentheses P minus Q close parentheses plus open square brackets open parentheses fraction numerator P minus 1 over denominator 2 end fraction close parentheses d close square brackets open parentheses Q minus R close parentheses plus open square brackets open parentheses fraction numerator Q minus 1 over denominator 2 end fraction close parentheses d close square brackets open parentheses R minus P close parentheses plus open square brackets open parentheses fraction numerator R minus 1 over denominator 2 end fraction close parentheses d close square brackets open parentheses P minus Q close parentheses equals 0 plus open square brackets fraction numerator P Q over denominator 2 end fraction minus Q over 2 minus fraction numerator P R over denominator 2 end fraction plus R over 2 plus fraction numerator R Q over denominator 2 end fraction minus R over 2 minus fraction numerator P Q over denominator 2 end fraction plus P over 2 plus fraction numerator R P over denominator 2 end fraction minus P over 2 minus fraction numerator Q R over denominator 2 end fraction plus Q over 2 close square brackets d equals 0 plus 0 equals 0

Answered by  | 7th Feb, 2014, 11:47: AM

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