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  • Question
  • The Sum of all terms of the arithmetic progression having 10th terms except for the 1st term, is 99, and except for the 6th term , 89. Find the 3rd terms of the progression if the sum of the 1st and the 5th term is equal to 10.


  • Options
  • A. 15
  • B. 5
  • C. 8
  • D. 10

  • Correct Answer


  • Explanation

    Let us assume the first term is a and common difference is d.
    Formula for nth term of Arithmetic Progression = a + ( n - 1 ) x d
    So first term t1 = a + ( n - 1 ) x d
    t1 = a + (1 - 1) x d = a + 0 x d = a
    Fifth term t5 = a + ( n - 1 ) x d = a + (5 - 1) x d = a + 4d
    According to question,
    Sum of the first term and the fifth term = 10
    t1 + t5 = 10
    ? a + a + 4d = 10
    ? 2a + 4d = 10
    ? a + 2d = 5.............................(1)

    Formula of sum of n terms for Arithmetic Progression,
    Sn = n/2[ 2a + ( n - 1 ) x d ]
    Put the value of n = 10, Since total number of terms is 10 .
    ? S10 = 10/2[ 2a + ( 10 - 1 ) x d ]
    ? S10 = 5[ 2a + 9 x d ] = 10a + 45d
    Again According to question,
    The sum of all terms of the Arithmetic Progression, except for the 1st term = 99
    S10 - first term = 99
    ? 10a + 45d - a = 99
    ? 9a +45d = 99
    ? a + 5d = 11.................................(2)
    Subtracts Equation (1) from Equation (2), we will get,
    ? a + 5d - a - 2d = 11 - 5
    ? 3d = 6
    ? d = 2
    Put the value of d in equation (1), we will get
    ? a + 2 x 2 = 5
    ? a + 4 = 5
    ? a = 5 - 4
    ? a = 1
    Since tn = a + ( n - 1) x d
    find the third term by putting the value of a , n and d. we will get,
    t3 = 1 + ( 3 - 1) x 2 = 1 + 2 x 2 = 1 + 4 = 5
    So 3rd term of Arithmetic Progression is 5.


  • More questions

    • 1. 
      Aarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type?

    • Options
    • A. 18 days
    • B. 21 days
    • C. 3 days
    • D. 6 days
    • Discuss
    • 2. 
      750.0003 ÷ 19.999 =?

    • Options
    • A. 49
    • B. 18
    • C. 22
    • D. 38
    • Discuss
    • 3. 
      105, 85, 60, 30, 0, - 45, - 90?

    • Options
    • A. 0
    • B. 85
    • C. -45
    • D. 60
    • Discuss
    • 4. 
      Let A = {1, 2, {3, 4}, 5}. Which of the following statements is true?

    • Options
    • A. {3, 4} ? A
    • B. {3, 4} ? A
    • C. 1 ? A
    • D. {1, 2, 5} ? A
    • Discuss
    • 5. 
      Two vessels A and B contains milk and water mixed in the ratio 5 : 3 and 2 : 3. When these mixtures are mixed to form a new mixture containing half milk and half water, they must be taken in the ratio ?

    • Options
    • A. 2 : 5
    • B. 3 : 5
    • C. 4 : 5
    • D. 7 : 3
    • Discuss
    • 6. 
      1, 2, 4, 8, 16, 32, 64, (...), 256?

    • Options
    • A. 148
    • B. 128
    • C. 154
    • D. 164
    • Discuss
    • 7. 
      A tree is 12 m tall and casts an an 8 m long shadow. At the same time, a flag pole caste a 100 m long shadow. How long is the flag pole?

    • Options
    • A. 150 m
    • B. 200 m
    • C. 125 m
    • D. 115 m
    • Discuss
    • 8. 
      8% of 96 =? of 1/25

    • Options
    • A. 19.2
    • B. 7.68
    • C. 1.92
    • D. None of these
    • Discuss
    • 9. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?

    • Options
    • A. Rs. 35
    • B. Rs. 245
    • C. Rs. 350
    • D. Cannot be determined
    • E. None of these
    • Discuss
    • 10. 
      If the hands of a clock coincide in every 65 minutes (true time), in 24 hours the clock will gain:

    • Options
    • A. 10 10 minutes. 143
    • B. 9 12 minutes. 143
    • C. 11 12 minutes. 143
    • D. 12 10 minutes. 143
    • Discuss


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