Home
Class 11
MATHS
Show that there is no A.P. which consist...

Show that there is no A.P. which consists of only distinct prime numbers.

Text Solution

Verified by Experts


The smallest prime numbers are
`2,3,5 .... `
In A.P, `a ^2` −`a ^1` should be equal to `a^3` −`a^2`
so, `3 - 2` must be equal to `5 - 3`
But they are not equal
This is not A.P
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    RD SHARMA|Exercise Solved Examples And Exercises|228 Videos

Similar Questions

Explore conceptually related problems

Which is the only even prime number?

Which is the only even prime number ?

Which of them is not in A.P ?

Find the number of 6 -digit numbers of the form ababab (in base 10) each of which is a product of exactly 6 distinct primes.

Set A consists of 4 distinct and set-B consists of 3 distinct elements. Number of functions that can be defined from a set A rarr B which are not onto is

Consider the following statements : 1. There exists only one prime number p such that (17 p + 1) is a square 2. If x is the product of 10 consecutive prime numbers starting from 2, then (x + 1) iş also a prime number Which of the above statements is/are correct?

Show that the number of primes in N is infinite.

RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
  1. Determine the number of terms in the terms in the A.P. 3,7,11…407. ...

    Text Solution

    |

  2. How many numbers of two digits are divisible by 7?

    Text Solution

    |

  3. Show that there is no A.P. which consists of only distinct prime nu...

    Text Solution

    |

  4. In the arithmetic progressions 2,5,8,… upto 50 terms and 3,5,7,9… upto...

    Text Solution

    |

  5. Find: 10 t h term of the A.P. 1,4,7,10..

    Text Solution

    |

  6. Find: nth term of the A.P. 13,8,3,-2,…

    Text Solution

    |

  7. Find: 18th term of the A.P. sqrt(2),\ 3sqrt(2),\ 5sqrt(2) ddot

    Text Solution

    |

  8. Evaluate (sqrt(3)+sqrt(2))^6-(sqrt(3)-sqrt(2))^6dot

    Text Solution

    |

  9. If the sequence an is A.P., show that a(m+n)+a(m-n)=2amdot\

    Text Solution

    |

  10. Which term of the A.P. 3,8,13… is 248?

    Text Solution

    |

  11. Which term of the A.P. 84,80,76… is 0?

    Text Solution

    |

  12. Which term of the A.P. 4,9,14… is 254?

    Text Solution

    |

  13. Is 68 as term of the A.P. 7,10,13,…?

    Text Solution

    |

  14. Is 302 a term of the A.P. 3,8,13,…?

    Text Solution

    |

  15. Which term of the sequence 24 ,\ 23 1/4,\ 22 1/2,\ 21 3/4 is the first...

    Text Solution

    |

  16. Which term of the sequence 12+8i ,\ 11+6i ,\ 10+4i ,... is (a) purely ...

    Text Solution

    |

  17. How many terms are there in the A.P. 7,10,13,…43?

    Text Solution

    |

  18. How many terms are there in the A.P. -1,\ -5/6,\ -2/3,-1/2,\ ,(10)/3?

    Text Solution

    |

  19. The first term of an AP. is 5, the common difference is 3 and the last...

    Text Solution

    |

  20. The 6th and 17th terms of an A.P. are 19 and 41 respectively, find t...

    Text Solution

    |