Home
Class 12
MATHS
If the fourth power of the common differ...

If the fourth power of the common difference of an A.P with integer entries is added to the product of any four consecutive of it, then the resulting sum is

A

an even integer

B

an odd integer

C

the square of an integer

D

the cube of an integer

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|213 Videos

  • QUADRATIC EQUATIONS AND EXPRESSION

    HIMALAYA PUBLICATION|Exercise Question Bank|129 Videos

Similar Questions

Explore conceptually related problems

Prove that the product of any two consecutive positive integers is divisible by 2.

What is the common difference of an A.P. in which a_(12) - a_(8) = 24 ?

Find the common difference of an AP whose first term is 4, last term is 49 and sum of all terms 265.

Find the common difference of an A.P. whose first term is (1)/(2) and the 8th term is (17)/(6) . Also write its 4th term.

In the A.P., the common difference is 3, first term is 1, then its tenth term is:

What is the common difference between the consecutive terms of an A.P.

A student read common difference of an A.P. as -2 instead of 2 and got the sum of first five terms as -5, the actual sum of first five terms is :

IF the sum of three consecutive terms of an A.P. is 21, then first the first term.

There are two sets A and B each of which consists of three numbers in AP whose sum is 15 and where D and d are the common differences such that D=1+d,dgt0. If p=7(q-p), where p and q are the product of the nymbers respectively in the two series. The value of p is

There are two sets A and B each of which consists of three numbers in AP whose sum is 15 and where D and d are the common differences such that D=1+d,dgt0. If p=7(q-p) , where p and q are the product of the nymbers respectively in the two series. The value of q is

HIMALAYA PUBLICATION-PROGRESSIONS-QUESTION BANK
  1. Let a^(n) be the nth term of the G.P. of positive numbers. Let sum(n=1...

    Text Solution

    |

  2. Let n ( gt 1 ) be a positive integer, the largest integer m such that ...

    Text Solution

    |

  3. If the fourth power of the common difference of an A.P with integer en...

    Text Solution

    |

  4. Consider an infinite geometric series with first term a and common rat...

    Text Solution

    |

  5. If the sum of the first 2n terms of the A.P. 2,5,8,"……….." is equal to...

    Text Solution

    |

  6. An infinite G.P. has first term 'x' and sum '5' , then x belongs to :

    Text Solution

    |

  7. If (a^(n)+b^(n))/(a^(n-1)+b^(n-1)) is an G.M between a and b then the ...

    Text Solution

    |

  8. If the sum of first n terms of an A.P. is cn^(2) , then the sum of squ...

    Text Solution

    |

  9. If (a+b)/(1-a b), b, (b+c)/(1-b c) are in A.P, then a, (1)/(b), c are ...

    Text Solution

    |

  10. If A(1), A(2) be two A.M's and G(1), G(2) be two G.M's between a and b...

    Text Solution

    |

  11. The sum pf 'n' terms of two arithmentic progressions are in the ratio ...

    Text Solution

    |

  12. If x=1+y+y^(2)+.. . to oo, then y is

    Text Solution

    |

  13. If A=1+r^(a)+r^(2 a)+r^(3 a)+.. . to oo and lebrge B=1+r^(b)+r^(2 b)+....

    Text Solution

    |

  14. The determinant : |(a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,...

    Text Solution

    |

  15. If a,b,c are in G.P.L, then the equations ax^(2) + 2bx + c = 0 0 and d...

    Text Solution

    |

  16. Every element of a G.P is positive and also every element is the sum o...

    Text Solution

    |

  17. If x gt 1 , y gt 1 , z gt 1 are in G.P. , then (1)/(1 + log x) , (1)/(...

    Text Solution

    |

  18. age0, then sum(n=1)^(infty)((a)/(a+1))^(n) equals

    Text Solution

    |

  19. If x,y,z are in A.P. and tan^(-1) x , tan^(-1) y and tan^(-1) z are a...

    Text Solution

    |

  20. The sum of three numbers in A.P. is 27 and the sum of their squares is...

    Text Solution

    |