Latest TCS Aptitude Question SOLUTION: What is the value of (2^2 + 4^2 + 6^2 + ... + 20^2 )? A) 542 B) 756 C) 1540 D) 968

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What is the value of (2^2 + 4^2 + 6^2 + ... + 20^2 )?
A) 542 B) 756 C) 1540 D) 968

Asked In TCS PRABIR (8 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

gourav  (8 years ago)

if we take 2^2 common of the sequence it reduces to 2^2(1^2+2^2+3^2+......+10^2) and now using the formula 1^2+2^2+3^2+........+n^2=n(n+1)(2n+1)/6 we get 2^2(10*11*21)/6=1540

Is this solution Helpfull? Yes (14) | No   

Amrita Sannigrahi  (8 years ago)

2^2(1^1+2^2+3^3+.....+10^2)=1540

Is this solution Helpfull? Yes (4) | No (1)  

Rinku Kumawat  (8 years ago)

first of all take 2^2 as common in all terms than the given expression can be rewritten as
2^2(1^2 + 2^2 + 3^2 + . . . + 10^2)
now as we know that (1^2 + 2^2 + 3^2 + . . . + n^2) = n(n+1)(2n+1)/6

so from this we can solve this...
2^2(10)(10+1)(2*10+1)/6 = 4*10*11*21/6 = 1540 ans.

Is this solution Helpfull? Yes (2) | No   

Pushan Sen  (8 years ago)

1540
4+16+36+64+100+144+196+256+324+400
1540

Is this solution Helpfull? Yes (2) | No (1)  

Rajanikanta Pradhan  (8 years ago)

2^2+2^2*2^2+2^2*3^2+2^2*4^2+..............2^2*10^2
2^2(1^2+2^2+3^2+......10^2)
4*5*11*7=1540

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SUNIT RANJAN  (8 years ago)

sum of even number square = 2n(n+1)(2n+1)/3
= 2*10(10+1)(2*10+1)/3
=1540

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Kr Sahas  (6 years ago)

Take 4 as common from series, u will get,
4(1^2+2^2+3^2+.....+10^2)
Then, use formula,
n(n+1)(2n+1)/6
Ans- 1540

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