Paragraph: Let V r denotes the sum of the first r terms of an arithmetic progression ( A P ) whose first term is r and the common difference is ( 2 r − 1 ) . Let T r = V r + 1 − V r − 2 and Q

Question

Paragraph: Let V r ​ denotes the sum of the first r terms of an arithmetic progression ( A P ) whose first term is r and the common difference is ( 2 r − 1 ) . Let T r ​ = V r + 1 ​ − V r ​ − 2 and Q r ​ = T r + 1 ​ − T r ​ for r = 1 , 2 , … Question: T r ​ is always

TestHub · Accepted Answer

V r + 1 ​ − V r ​ = ( r + 1 ) 3 − r 3 − 2 1 ​ [ ( r + 1 ) 2 − r 2 ] + 2 1 ​ ( 1 ) ∴ T r ​ ​ = 3 r 2 + 2 r + 1 = 3 r 2 + 2 r − 1 = ( r + 1 ) ( 3 r − 1 ) ​ which is a composite number.

Mathematics - Sequence & Series Question with Solution | TestHub

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