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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. 
      Find the present worth of a bill of Rs. 2420 due 2 years later at 10% compound interest. Also find the true discount?

    • Options
    • A. Rs. 2000, Rs. 420
    • B. Rs. 2200, Rs. 520
    • C. Rs. 2100, Rs. 460
    • D. None of these
    • Discuss
    • 2. In the following question, four groups of three numbers are given. In each group the second and third number are related to the first number by a Logic/Rule/Relation. Three are similar on basis of same Logic/Rule/Relation. Select the odd one out from the given alternatives.

    • Options
    • A. (9, 11, 14)
    • B. (13, 15, 18)
    • C. (17, 19, 22)
    • D. (21, 23, 28)
    • Discuss
    • 3. Find the odd word/letters/numbers pair from the given alternatives.

    • Options
    • A. 41 - 72
    • B. 12 - 30
    • C. 51 - 42
    • D. 11 - 20
    • Discuss
    • 4. Find the odd man out. 253, 136, 352, 324, 631, 244

    • Options
    • A. 324
    • B. 136
    • C. 352
    • D. 631
    • Discuss
    • 5. Select the odd word from the given alternatives.

    • Options
    • A. Stream
    • B. Rivulet
    • C. River
    • D. Valley
    • Discuss
    • 6. Select the odd word from the given alternatives.

    • Options
    • A. Chair
    • B. Sofa
    • C. Couch
    • D. Television
    • Discuss
    • 7. Find the odd number in the following number series? 24, 4, 13, 41, 151, 640

    • Options
    • A. 4
    • B. 640
    • C. 41
    • D. 13
    • Discuss
    • 8. Find the odd term from the given series of numbers ? 125, 127, 130, 135, 142, 153, 165 ?

    • Options
    • A. 153
    • B. 165
    • C. 142
    • D. 127
    • Discuss
    • 9. What comes next in this sequence 196, 169, 144, 121, 100, 81, ?

    • Options
    • A. 77
    • B. 74
    • C. 67
    • D. 64
    • Discuss
    • 10. Find out the odd word/letters/number/number pair from the given alternatives.

    • Options
    • A. LJH
    • B. XUS
    • C. VTR
    • D. FDB
    • Discuss


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