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Given 1³ + 2³ + 3³ + ... + 10³ = 3025 then 2³ + 4³ + 6³ + ...+ 20³ is equal to
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- 6050
- 9075
- 12100
- 24200
- 6050
Correct Option: D
It is given, 1³ + 2³ + 3³ + ... + 10³ = 3025 ........( 1 )
Now, 2³ + 4³ + 6³ + ... + 20³ = (1 × 2)³ + (2 × 2)³ + (2 × 3)³ + ... + (2 × 10)³
2³ + 4³ + 6³ + ... + 20³ = 2³ [1³ + 2³ + 3³ + ... + 10³]
Using the value of equation ( 1 ) , we get
∴ 2³ + 4³ + 6³ + ... + 20³ = 8 × 3025 = 24200
