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 Let A be the sum of the first 20 terms and ' B ' be the sum of the first 40-  terms of the series 12+2.22+32+2.42+52+2.62+.. If B2A=100λ then λ is 

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a
248
b
464
c
496
d
232

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detailed solution

Correct option is A

B-2A=∑n=140an-2∑n=120an=∑n=2140an-∑n=120anB-2A=212+2.222+232+...+402−12+2.22+32+2.42+...+202=20(22+2.24+26+2.28+..+60)=20{(22+24+26+..+60)⏟20 terms+(24+28+..+60)⏟10 terms}=20202(22+60)+102(24+60)=10(20.82+10.84)=10(1640+840)=100(164+84)=100×248→λ=248


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If the sum of first n terms of an AP is cn2, then the sum of squares of these  n terms is 


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