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Question

# Let a cricket player played n (n>1) matches during his career. If Tr represents the runs made by the player in rth match such that T1=6 and Tr=3Tr–1+6r for 2≤r≤n, then the runs scored by him in 100 matches is

A
35[46100531001]
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B
25[4610053100+1]
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C
35[46995399+1]
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D
35[4610053100+1]
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Solution

## The correct option is D 35[4⋅6100−5⋅3100+1]Given : Tr=3Tr–1+6r ⇒Tr−3Tr–1=6r⇒Tr3r−Tr−13r−1=2r⇒n∑r=2(Tr3r−Tr−13r−1) =T232−T13 +T333−T232 +T434−T333 ⋮ +Tn3n−Tn−13n−1⇒n∑r=2(Tr3r−Tr−13r−1)=Tn3n−T13 Therefore, Tn3n−T13=n∑r=22r ⇒Tn3n−2=22(2n−1−1)⇒Tn3n=2(2n−1)⇒Tn=2(6n−3n) So, Sn=2(n∑16r−n∑13r) ⇒Sn=2[65(6n−1)−32(3n−1)]⇒Sn=35[4⋅6n−5⋅3n+1] Hence, the runs scored by the player =35[4⋅6100−5⋅3100+1]

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