Home
Class 12
MATHS
The largest term common to the sequences...

The largest term common to the sequences `1, 11 , 21 , 31 , to100` terms and `31 , 36 , 41 , 46 , to100` terms is `381` b. `471` c. `281` d. none of these

A

381

B

471

C

281

D

521

Text Solution

Verified by Experts

The correct Answer is:
D
`100^(th)` term of 1,11,21,31,.. Is 1+(100-1)10=991.
`100^(th)` term of 31,36,41,46,.. Is 31+(100-1)5=526.
Let the largest common term be 526. Then,
`526=31+(n-1)10`
or n=50.5
But n is an integer, hence n=50. Hence, the largest common term is `31+(50-1)10=521`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Multiple & Comprehension)|66 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise EXERCIESE ( MULTIPLE CORRECT ANSWER TYPE )|2 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.9|9 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

The number of terms common between the series 1+ 2 + 4 + 8..... to 100 terms and 1 + 4 + 7 + 10 +... to 100 terms is

The 100^(th) term of the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ……. is

The next two terms of the given sequene 1, 3, 7, 15, 31,… A)4254 B)62124 C)64128 D)63127

The sum 1+3+7+15+31+...to100 terms is 2^(100)-102 b b. 2^(99)-101 c. 2^(101)-102 d. none of these

If the coefficients of 5th, 6th , and 7th terms in the expansion of (1+x)^n are in A.P., then n= a. 7 only b. 14 only c. 7 or 14 d. none of these

If the coefficients of rth and (r+1)t h terms in the expansion of (3+7x)^(29) are equal, then r equals a. 15 b. 21 c. 14 d. none of these

Find the t_2 of the following sequence for which S_1 = 2,S_2 = 12 and S_3 = 36 A)24 B)2 C)10 D)none of these

The first term of an infinite geometric series is 21. The second term and the sum of the series are both positive integers. Then which of the following is not the possible value of the second term 12 b. 14 c. 18 d. none of these

The largest term in the sequence a_n=(n^2)/(n^3+200) is given by (a) (529)/(49) (b) 8/(89) (c) (49)/(543) (d) none of these

If A.M., G.M., and H.M. of the first and last terms of the series of 100 , 101 , 102 ,...n-1,n are the terms of the series itself, then the value of n is '(100

CENGAGE-PROGRESSION AND SERIES-Exercise (Single)
  1. If three positive real numbers a, b, c are in A.P and abc = 4, then th...

    Text Solution

    |

  2. If log(2)(5.2^(x)+1),log(4)(2^(1-x)+1) and 1 are in A.P,then x equals

    Text Solution

    |

  3. The largest term common to the sequences 1, 11 , 21 , 31 , to100 term...

    Text Solution

    |

  4. In any A.P. if sum of first six terms is 5 times the sum of next six t...

    Text Solution

    |

  5. If the sides of a right angled triangle are in A.P then the sines of t...

    Text Solution

    |

  6. If a ,1/b ,a n d1/p ,q ,1/r from two arithmetic progressions of the co...

    Text Solution

    |

  7. Suppose that F(n +1) =( 2f(n)+1)/2 for n = 1, 2, 3,.....and f(1)= 2 ...

    Text Solution

    |

  8. Consider an A. P .a1,a2,a3,..... such that a3+a5+a8 =11and a4+a2=-2 th...

    Text Solution

    |

  9. If a(1),a(2),a(3),…. are in A.P., then a(p),a(q),q(r) are in A.P. if p...

    Text Solution

    |

  10. Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equ...

    Text Solution

    |

  11. If the sum of m terms of an A.P. is same as the sum of its n terms, th...

    Text Solution

    |

  12. If S(n) denotes the sum of n terms of an A.P., S(n +3) - 3S(n + 2) + 3...

    Text Solution

    |

  13. The first term of an A.P. is a and the sum of first p terms is zero, s...

    Text Solution

    |

  14. If Sn denotes the sum of first n terms of an A.P. and (S(3n)-S(n-1))/(...

    Text Solution

    |

  15. The number of terms of an A.P. is even; the sum of the odd terms is 24...

    Text Solution

    |

  16. The number of terms of an A.P. is even; the sum of the odd terms is 24...

    Text Solution

    |

  17. Concentric circles of radii 1,2,3,. . . . ,100 c m are drawn. The inte...

    Text Solution

    |

  18. If a1,a2,a3….a(2n+1) are in A.P then (a(2n+1)-a1)/(a(2n+1)+a1)+(a2n-...

    Text Solution

    |

  19. If a(1), a(2), ……., a(n) are in A.P. with common differece d != 0, the...

    Text Solution

    |

  20. ABC is a right-angled triangle in which angleB=90^(@) and BC=a. If n p...

    Text Solution

    |