Home
Class 12
MATHS
Let a(1),a(2),a(3)"……." be an arithmetic...

Let `a_(1),a_(2),a_(3)"……."` be an arithmetic progression and `b_(1), b_(2), b_(3), "……."` be a geometric progression sequence `c_(1),c_(2),c_(3,"…."` is such that `c_(n)= a_(n) + b_(n) AA n in N`. Suppose `c_(1) = 1, c_(2) = 4, c_(3) = 15` and `c_(4) = 2`.
The value of sum of `sum_(i = 1)^(20) a_(i)` is equal to

A

480

B

770

C

960

D

1040

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos
  • EQUATIONS

    RESONANCE|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |7 Videos

Similar Questions

Explore conceptually related problems

Let a_(1),a_(2),a_(3)..... be an arithmetic progression and b_(1),b_(2),b_(3)...... be a geometric progression.The sequence c_(1),c_(2),c_(3),... is such that c_(n)=a_(n)+b_(n)AA n in N. suppose c_(1)=1.c_(2)=4.c_(3)=15 and c_(4)=2. The common ratio of geometric progression is equal to

If a_(1),a_(2),a_(3),…a_(n+1) are in arithmetic progression, then sum_(k=0)^(n) .^(n)C_(k.a_(k+1) is equal to

Let A be nxxn matrix given by A=[(a_(11),a_(12),a_(13)……a_(1n)),(a_(21),a_(22),a_(23)…a_(2n)),(vdots, vdots, vdots),(a_(n1),a_(n2),a_(n3).a_("nn"))] Such that each horizontal row is arithmetic progression and each vertical column is a geometrical progression. It is known that each column in geometric progression have the same common ratio. Given that a_(24)=1,a_(42)=1/8 and a_(43)=3/16 The value of lim_(nto oo)sum_(i=1)^(n)a_(ii) is equal to

For an increasing geometric sequence a_(1),a_(2),a_(3),...,a_(n) if a_(6)=4a_(4) & a_(0)-a_(7)-192 and sum_(1=4)^(n)a_(i)=1016 ,then n is

Let a_(1),a_(2),a_(3)... and b_(1),b_(2),b_(3)... be arithmetic progressions such that a_(1)=25,b_(1)=75 and a_(100)+b_(100)=100 then the sum of first hundred terms of the progression a_(1)+b_(1)a_(2)+b_(2) is

Let a_(1), a_(2), a_(3)... be a sequance of positive integers in arithmetic progression with common difference 2. Also let b_(1),b_(2), b_(3)...... be a sequences of posotive intergers in geometric progression with commo ratio 2. If a_(1)=b_(1)=c_(2) . then the number of all possible values of c, for which the equality. 2(a_(1)+a_(2).+.....+a_(n))=b_(1)+b_(2)+....+b_(n) holes for same positive integer n, is

If (a_(1)+ib_(1))(a_(2)+ib_(2))………………(a_(n)+ib_(n))=A+iB , then sum_(i=1)^(n) tan^(-1)(b_(i)/a_(i)) is equal to

RESONANCE-DPP-QUESTION
  1. In the given figure (circle), P T=5,P D=7a n dP A=2, then the value of...

    Text Solution

    |

  2. Let a1,a2,a3..... be an arithmetic progression and b1,b2,b3...... be ...

    Text Solution

    |

  3. Let a(1),a(2),a(3)"……." be an arithmetic progression and b(1), b(2), b...

    Text Solution

    |

  4. If x = tan'(pi)/(18) then 3x^(6) - 27x^(4) + 33x^(2) is equal to -

    Text Solution

    |

  5. The sequence form by common terms of 17,21,25,"….." & 16,21,26,"…." ha...

    Text Solution

    |

  6. If Sn denotes the sum of first n terms of an arithmetic progression an...

    Text Solution

    |

  7. If log(x)a, a^(x//2), log(b)x are in G.P. then x is equal to

    Text Solution

    |

  8. Solve |(x^2-5x+4)/(x^2-4)|<=1

    Text Solution

    |

  9. Solve the following equations : (i) |x^(2)-2| = 2 |x-3| (ii) |x^(2...

    Text Solution

    |

  10. The variable x satisfying the equation |sinxcosx|+sqrt(2+tan^2+cot^2x)...

    Text Solution

    |

  11. Let A0A1A2A3A4A5 be a regular hexagon inscribed in a circle of unit ra...

    Text Solution

    |

  12. Let the n^(th) term of a series be given by tn = (n^2 -n-2)/(n^2+3n),n...

    Text Solution

    |

  13. a, b, c are the first three terms of geometric series. If the H.M. of ...

    Text Solution

    |

  14. Consider an A.P. a(1), a(2), "……"a(n), "……." and the G.P. b(1),b(2)"…....

    Text Solution

    |

  15. If sum(r=1)^(n) r(r+1) = ((n+a)(n+b)(n+c))/(3), where a gt b gt c, the...

    Text Solution

    |

  16. If 5 sinx cosy = 1 and 4 tan x = tany, then

    Text Solution

    |

  17. Solve : (i) -2 le ||x^(2) +1| -3 | le 7 (ii) |x^(2) - 4x| le 5

    Text Solution

    |

  18. Number of roots of equation 3^(|x|)-|2-|x||=1 is a. 0 b. 2 c. 4 d. 7

    Text Solution

    |

  19. Study carefully the graph of a certain function The graph corresp...

    Text Solution

    |

  20. If the r^(th) term of a series is 1 + x + x^2 + .......+ x^(r-1) , the...

    Text Solution

    |