Pls answer this: Let Tr be the rth term of a sequence for r = 1,2,3, - Maths - Sequences and Series

Question

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 ​

Shivam Mishra · Accepted Answer

Dear Student,
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-T6T5n⇒arn-1r-1=1-ar5ar4n⇒arn-1r-1=1-rn⇒arn-1r-1=-rn-1⇒a=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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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 ​

Pls answer this: Let T_r be the r^th term of a sequence for r = 1,2,3,..... such that and T_r > 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