All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
CA Foundation Exam  >  CA Foundation Questions  >  The sum of an A.P whose first Term is -4 and ... Start Learning for Free
SaveJoin the Discussion on the App
The sum of an A.P whose first Term is -4 and last term is 146 is 7171.?
Clear all your CA Foundation doubts with EduRev
Most Upvoted Answer
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.
Explore Courses for CA Foundation exam

Top Courses for CA FoundationView all

Top Courses for CA Foundation

The sum of an A.P whose first Term is -4 and last term is 146 is 7171.?
Question Description
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.?.
Solutions for The sum of an A.P whose first Term is -4 and last term is 146 is 7171.? in English & in Hindi are available as part of our courses for CA Foundation. Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of The sum of an A.P whose first Term is -4 and last term is 146 is 7171.? defined & explained in the simplest way possible. Besides giving the explanation of The sum of an A.P whose first Term is -4 and last term is 146 is 7171.?, a detailed solution for The sum of an A.P whose first Term is -4 and last term is 146 is 7171.? has been provided alongside types of The sum of an A.P whose first Term is -4 and last term is 146 is 7171.? theory, EduRev gives you an ample number of questions to practice The sum of an A.P whose first Term is -4 and last term is 146 is 7171.? tests, examples and also practice CA Foundation tests.
Explore Courses for CA Foundation exam

Top Courses for CA Foundation

Explore Courses

Suggested Free Tests

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup