Train Your A.P
Algebra
Level
2
If a,b,c are the p th , q th and r th terms respectively of an Arithmetic progression(A.P) . Find the value of a(q-r) + b(r-p) + c(p-q) . Please follow me for more problems like this.
The answer is 0.
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Let a = g + d ( p − 1 ) , b = g + d ( q − 1 ) , c = g + d ( r − 1 ) So, the expression of interest is: ( g + d ( p − 1 ) ) ( q − r ) + ( g + d ( q − 1 ) ) ⋅ ( r − p ) + ( g + d ( r − 1 ) ) ( p − q ) = g ⋅ ( q − r + r − p + p − q ) + d ⋅ [ ( p − 1 ) ( q − r ) + ( q − 1 ) ( r − p ) + ( r − 1 ) ( p − q ) = g ⋅ ( 0 ) + d ⋅ [ p q − q − r + r + q r − p q − r + p + r p − q r − p + q ] = 0 + d ⋅ ( 0 ) = 0