# Aptitude  Number series  Practice Q&A

81. Which one of the following is NOT a sum of cubes of the first n natural numbers?

 1 23409 8521 441

82. Sum of first n even numbers = ?

 Sum of first n odd number + n Sum of first n natural numbers - Sum of first n odd numbers Sum of first n odd numbers - n Sum of first n odd numbers - Sum of first n natural numbers

83. Among the following relationships, which one is INCORRECT?

 Sum of cubes of first n natural numbers = [Sum of first n natural numbers]$^{2}$ Sum of first n even numbers = Sum of first n odd numbers + n Sum of first n natural numbers = 2 × Sum of first n even numbers Sum of squares of first n natural numbers = 2 × Sum of squares of first n even numbers

84. If you find the sum of the squares of the first n natural numbers, which n gives you a sum of 1240?

 12 13 15 18

85. Which one of the following is NOT a sum of squares of the first n natural numbers?

 420 385 506 650

86. The ratio of squares of first n natural numbers to square of sum of first n natural numbers is 17:325. The value of n is:

 15 25 30 35

87. What is the sum of the squares of the first 20 natural numbers (1 to 20)?

 2870 5650 2000 44100

88. The sum of the squares of the first 15 positive integers is equal to 1240. What is the sum of the squares of the second 15 positive integers?

 2480 3490 6785 8215

89. If the sum of the first n positive integers is x, then which of the following is the sum of the first 2n even positive integers?

 $2x + 2n^{2}$ $3x + 4n^{2}$ $4x + n^{2}$ $4x + 2n^{2}$