Home
Class 11
MATHS
Let a1,a2,a3,.......a11 be real number s...

Let `a_1,a_2,a_3,.......a_11` be real number satisfying `a_1=15,27-2a_2gt0 anda_k=2a_(k-1)-a_(k-2) ` for k=3,4,.....11. If `(a_1^2+a_2^2+......a_11^2)/11=90,` then the value of `(a_1 +a_2+.....a_11)/11` is equal to

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    PATHFINDER|Exercise QUESTION BANK|41 Videos

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

Similar Questions

Explore conceptually related problems

If a_1,a_2,.....a_n are in H.P., then the expression a_1a_2 + a_2a_3 + ... + a_(n-1)a_n is equal to

Let a_1,a_2 ,a_3 ...... be an A.P. Prove that sum_(n=1)^(2m)(-1)^(n-1)a_n^2=m/(2m-1)(a_1^2-a_(2m)^2) .

If a_1+a_2+a_3+......+a_n=1 AA a_i > 0, i=1,2,3,......,n , then find the maximum value of a_1 a_2 a_3 a_4 a_5......a_n .

The Fibonacci sequence is defined by 1=a_1=a_2 and a_n=a_(n-1)+a_(n-2,)n > 2. Find (a_(n+1))/(a_n) , for n=5.

A sequence of no. a_1,a_2,a_3 ..... satisfies the relation a_n=a_(n-1)+a_(n-2) for nge2 . Find a_4 if a_1=a_2=1 .

Let a_1 , a_2 , a_3,.... be terms of an A.P. if (a_1 + a_2 +....+ a_p)/(a_1 + a_2 +...+ a_q) = p^2/q^2. p ne q then a_6/a_21 equals

If a_1,a_2,.....a_n are positive real number whose product is a fixed number c, then the minimum value of a_1+a_2+......+a_(n-1)+a_n is

If the sequence a_1, a_2, a_3,....... a_n ,dot forms an A.P., then prove that a_1^2-a_2^2+a_3^2-a_4^2+.......+ a_(2n-1)^2 - a_(2n)^2=n/(2n-1)(a_1^2-a_(2n)^2)

Consider an A.P. a_1, a_2, a_3,......... such that a_3+a_5+a_8=11 and a_4+a_2=-2, then the value of a_1+a_6+a_7 is (a). -8 (b). 5 (c). 7 (d). 9

If a_1 and a_2 are two non-collinear unit vectors and if |a_1+a_2|=sqrt(3) , then the value of (a_1-a_2)*(2a_1+a_2) is

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. If a,b,c ,d are distinct integer in AP such that d=a^2+b^2+c^2, then a...

    Text Solution

    |

  2. If log2(a+b)+log2(c+d)ge4 . Then the minimum value of the expression a...

    Text Solution

    |

  3. Let a1,a2,a3,.......a11 be real number satisfying a1=15,27-2a2gt0 anda...

    Text Solution

    |

  4. The interior angles of a polygon are in arithmetic progression. The sm...

    Text Solution

    |

  5. Find the sum of the first n terms of the series 1^3+3.2^2+3^3+3.4^2+5^...

    Text Solution

    |

  6. Find the sum of the first n terms of the series 1^3+3.2^2+3^3+3.4^2+5^...

    Text Solution

    |

  7. Does there exist a GP containing 27,8 and 12 as three of its terms ? I...

    Text Solution

    |

  8. The sum of the squares of three distinct real numbers, which are in GP...

    Text Solution

    |

  9. Prove that the three successive terms of a GP will form the sides of ...

    Text Solution

    |

  10. If (m+1)^th ,(n+1)^th and (r+1)^th terms in AP are in GP m,n,r are in ...

    Text Solution

    |

  11. If p be the first of n arithmetic means between two numbers and q be t...

    Text Solution

    |

  12. Show that 1^4/13+2^4/3.5+3^4/5.7+.....+n^4/((2n-1)(2n+1))=(n(4n^2+6n+5...

    Text Solution

    |

  13. Solve the following equations for x and y log10xx+1/2log10xx+1/4log10x...

    Text Solution

    |

  14. Find the sum of the series 1/1.3+2/(1.3.5)+3/(1.3.5.7)...upto infinit...

    Text Solution

    |

  15. If sum(r=1)^nTr =n/8(n+1)(n+2)(n+3) then find sum(r=1)^n1/Tr

    Text Solution

    |

  16. If 1,log9(3^(1-x)+2) and log3(4.3^x-1) are in AP , then x is equal to

    Text Solution

    |

  17. If the sum of the first 2n terms of the AP 2,5,8.....is equal to the s...

    Text Solution

    |

  18. If xin R , the number 5^(1+x)+5^(1-x),a/2,25^x+25^-xform an AP , then ...

    Text Solution

    |

  19. If an AP a7=9 and a1a2a7 is least , then common difference is

    Text Solution

    |

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

    Text Solution

    |