Arithmetic Progressions - Olympiad Level MCQ, Class 10 Mathematics - Class 10 MCQ

A student read common difference of an AP is – 2 instead of 2 and got the sum of first five terms as – 5. The actual sum of first five terms is :

The sum of n terms of two A.P's are in the ratio of (7n + 1) : (4n + 27). The ratio of their 11th terms is –

If 1² + 2² + 3² + ..... n² = 1015, then the value of n is :

The sum of the series  + ... upto 9 terms is :

The sum of first n odd natural numbers is :

If the roots of the equation x³ – 12x² + 39x – 28 = 0 are in A.P., then their common difference will be :

If A.M between two numbers is 5 and their G.M. is 4, then their H.M. is :

If A is the single A.M. between two numbers a and b and S is the sum of n A.M.'s between them, then S/A depends upon :

If the A.M. between the roots of a quadratic equation is 8 and the G.M. is 5, then the equation is :

If c is the harmonic mean between a and b, then   is equal to :

If a,b,c,d,e,f are in A.P. then e–c is equal to :

20th term of the series :   + ......... is :

If the value of 1³ + 2³ + 3³ + ...+n³ = 2025, then the value of 1 + 2 + 3 +...+ n is :

If the value of 1 + 2 + 3 +... + n is 55, then the value of 1³ + 2³ + 3³ + .... + n³  is :

The nth term of the series 1 +   +............... is :

1² + 1 + 2² + 2 + 3² + 3 + ... + n² + n is equal to :

The next term of the sequence (1/4,1/36,1/144)   ............ is :

If the sum of first n natural numbers is one-fifth of the sum of their squares, then n equals :

The nth term of the series 1 + 3 + 6 + 10 + 15 + ... is :

The sum of the series 1² + 1 + 2² + 2 + 3² + 3 + ... + up to n terms is :

The nth term of the sequence

The sum of n terms of the series (1² – 2²) + (3² – 4²) + (5² – 6²) +... is :