Statement 1: If nonzero real a,b,c satisfy 3 ( a 2 + b 2 + c 2 + 1 ) = 2 ( a + b + c + ab + bc + ca ) , then a,b,c form both an A.P. and a G.P. Statement 2: Any sequence of equal, nonzero terms forms

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Statement 1: If nonzero real a,b,c satisfy 3 ( a 2 + b 2 + c 2 + 1 ) = 2 ( a + b + c + ab + bc + ca ) , then a,b,c form both an A.P. and a G.P. Statement 2: Any sequence of equal, nonzero terms forms both an A.P. and a G.P.

TestHub · Accepted Answer

Rearranging gives ( a − 1 ) 2 + ( b − 1 ) 2 + ( c − 1 ) 2 + ( a − b ) 2 + ( b − c ) 2 + ( c − a ) 2 = 0 . Thus a = b = c = 1 ; Statement 2 gives the asserted progressions.

Mathematics - Sequence & Series Question with Solution | TestHub

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