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The sum of an A.P whose first Term is -4 and last term is 146 is 7171.?
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The sum of an A.P whose first Term is -4 and last term is 146 is 7171....
Given:

  • First term of A.P (a) = -4

  • Last term of A.P (l) = 146

  • Sum of A.P (S) = 7171



To Find: Common difference of A.P (d)

Explanation:

  • We know that the sum of an A.P is given by the formula: S = n/2 [2a + (n - 1)d], where n is the number of terms in the A.P, a is the first term, l is the last term, and d is the common difference.

  • From the given information, we can write the following equations:


    • a = -4

    • l = 146

    • S = 7171


  • Substituting these values in the formula for the sum of A.P, we get:


    • S = n/2 [2a + (n - 1)d]

    • 7171 = n/2 [2(-4) + (n - 1)d]

    • 7171 = -2n + nd + 8n - 8d

    • 7171 = 6n - 10d


  • We also know that the last term of an A.P is given by the formula: l = a + (n - 1)d

  • Substituting the values of a and l, we get:


    • 146 = -4 + (n - 1)d

    • 150 = (n - 1)d

    • d = 150/(n - 1)


  • Substituting this value of d in the equation for S, we get:


    • 7171 = 6n - 10(150/(n - 1))

    • Simplifying this equation, we get:

    • 7171(n - 1) = 6n(n - 1) - 1500

    • 7171n - 7171 = 6n^2 - 6n - 1500

    • 6n^2 - 7177n + 5671 = 0

    • Solving this quadratic equation, we get:

    • n = 121 or n = -78.5 (rejecting negative value)


  • Substituting this value of n in the equation for d, we get:


    • d = 150/(n - 1)

    • d = 150/120

    • d = 5/4


  • Therefore, the common difference of the A.P is 5/4.
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The sum of an A.P whose first Term is -4 and last term is 146 is 7171.?
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The sum of an A.P whose first Term is -4 and last term is 146 is 7171.? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sum of an A.P whose first Term is -4 and last term is 146 is 7171.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of an A.P whose first Term is -4 and last term is 146 is 7171.?.
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