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This mock test of Arithmetic Progressions - Olympiad Level MCQ, Class 10 Mathematics for Class 10 helps you for every Class 10 entrance exam.
This contains 25 Multiple Choice Questions for Class 10 Arithmetic Progressions - Olympiad Level MCQ, Class 10 Mathematics (mcq) to study with solutions a complete question bank.
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QUESTION: 1

For a series whose nth term is , the sum of r terms is :

Solution:

QUESTION: 2

15th term of the A.P., x – 7, x – 2, x + 3,.... is

Solution:

[Sol^{n}: a_{n} = a + (n - 1)× d

where d = x – 2 - x + 7 = 5, a = x - 7

⇒a_{15} =(x - 7) + (15 - 1) ×5 = (x - 7) + 14 ×5

⇒a_{15} = x - 7 + 70 = x + 63]

QUESTION: 3

The sum of first 24 terms of an A.P. a_{1}, a_{2}, a_{3},...; if it is known that a_{1} + a_{5} + a_{10} + a_{15} + a_{20} + a_{24} = 225, is equal to :

Solution:

QUESTION: 4

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 :

Solution:

QUESTION: 5

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 –

Solution:

QUESTION: 6

If 1^{2} + 2^{2} + 3^{2} + ..... n^{2} = 1015, then the value of n is :

Solution:

QUESTION: 7

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

Solution:

QUESTION: 8

The sum of first n odd natural numbers is :

Solution:

QUESTION: 9

If the roots of the equation x^{3} – 12x^{2} + 39x – 28 = 0 are in A.P., then their common difference will be :

Solution:

QUESTION: 10

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

Solution:

QUESTION: 11

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 :

Solution:

Given, A=a+b/2--------------------eq-1

we know that , s= n/2(a+l)

here,a=a,l=b

so, s=n/2(a+b)---------------------------eq-2

so, s=n[a+b/2]

A=a+b/2

equate 1&2

then , S/n=A

S/A=n

QUESTION: 12

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

Solution:

QUESTION: 13

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

Solution:

QUESTION: 14

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

Solution:

QUESTION: 15

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

Solution:

QUESTION: 16

If the value of 1^{3} + 2^{3} + 3^{3} + ...+n^{3} = 2025, then the value of 1 + 2 + 3 +...+ n is :

Solution:

QUESTION: 17

If the value of 1 + 2 + 3 +... + n is 55, then the value of 1^{3} + 2^{3} + 3^{3} + .... + n^{3} is :

Solution:

QUESTION: 18

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

Solution:

QUESTION: 19

1^{2} + 1 + 2^{2} + 2 + 3^{2} + 3 + ... + n^{2} + n is equal to :

Solution:

QUESTION: 20

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

Solution:

QUESTION: 21

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

Solution:

QUESTION: 22

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

Solution:

QUESTION: 23

The sum of the series 1^{2} + 1 + 2^{2} + 2 + 3^{2} + 3 + ... + up to n terms is :

Solution:

QUESTION: 24

The nth term of the sequence

Solution:

QUESTION: 25

The sum of n terms of the series (1^{2} – 2^{2}) + (3^{2 }– 4^{2}) + (5^{2} – 6^{2}) +... is :

Solution:

### Class 10 Mathematics - Arithmetic Progressions

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### Class 10 Arithmetic progressions

Video | 12:12 min

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