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08 Jan 2020, 02:15
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B
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Difficulty:
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Question Stats:
72% (01:26) correct
28%
(01:40)
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If \(1^2+2^2+3^2+...+9^2=285\), \(3^2+6^2+9^2+12^2+15^2+...+27^2=?\)
(A) 855
(B) 2,565
(C) 7,695
(D) 23,085
(E) 69,255
08 Jan 2020, 02:44
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\(1^2+2^2+3^2+...+9^2=285\),
\(3^2+6^2+9^2+12^2+15^2+...+27^2=?\)
Taking \(3^2\) common from \(3^2+6^2+9^2+12^2+15^2+...+27^2\)
We get: \(3^2\)(\(1^2+2^2+3^2+...+9^2\))
replacing the value of \(1^2+2^2+3^2+...+9^2=285\)
\(3^2*285\)
we get 2,565 (B is the Winner)
\(3^2+6^2+9^2+12^2+15^2+...+27^2=?\)
Taking \(3^2\) common from \(3^2+6^2+9^2+12^2+15^2+...+27^2\)
We get: \(3^2\)(\(1^2+2^2+3^2+...+9^2\))
replacing the value of \(1^2+2^2+3^2+...+9^2=285\)
\(3^2*285\)
we get 2,565 (B is the Winner)
08 Jan 2020, 04:59
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Quote:
If \(1^2+2^2+3^2+...+9^2=285\), \(3^2+6^2+9^2+12^2+15^2+...+27^2=\)?
(A) 855
(B) 2,565
(C) 7,695
(D) 23,085
(E) 69,255
(A) 855
(B) 2,565
(C) 7,695
(D) 23,085
(E) 69,255
\(3^2+6^2+9^2+12^2+15^2+...+27^2\)
\(3^2+3^22^2+3^23^2+3^22^4+3^25^2+...+3^23^4\)
\(3^2(1+2^2+3^2+2^4+5^2+2^23^2...+3^4)\)
\(3^2(1+4+9+16+25+36…81)\)
\(3^2(285)=2565\)
Ans (B)
