Pls answer this: Let Tr be the rth term of a sequence for r = 1,2,3,..... such that  and Tr > 0  N. If sum of first n terms of this sequence is  and maximum value of T5 is  where p & q are coprime numbers then value of (p + q) is- (1) 3381 (2) 3268 (3) 3496 (4) 3167  ​  

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Please find below the solution to the asked query:

We haveTr+2Tr+1=Tr+1TrHence given sequence is a G.P.Let a be first term and r be common ratioSum of n terms=arn-1r-1According to questionarn-1r-1=1-T6T5narn-1r-1=1-ar5ar4narn-1r-1=1-rnarn-1r-1=-rn-1a=1-rT5=ar4=1-rr4T5=r4-r5Differentiate with respect to rDT5dr=4r3-5r4=5r345-rCritical points are r=0 and r=45 and method of interval we can seethat r=45 is point maxima.T5=1-rr4T5max=1-45454=2563125=pqp+q=256+3125=3381 Answer

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