Class 10 Exam > Class 10 Questions > Sum of first four terms of an AP is 56 and su...
Start Learning for Free
Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms?
Most Upvoted Answer
Sum of first four terms of an AP is 56 and sum of last four term of an...
Community Answer
Sum of first four terms of an AP is 56 and sum of last four term of an...
Given Information
- Sum of the first four terms of an AP is 56.
- Sum of the last four terms of the same AP is 112.
- The first term (a) is 11.
Formulas and Definitions
- The sum of the first n terms of an AP can be calculated using the formula:
Sum = n/2 * (2a + (n-1)d),
where 'a' is the first term, 'd' is the common difference, and 'n' is the number of terms.
Calculating the Sum of the First Four Terms
- For the first four terms:
- n = 4
- Sum = 4/2 * (2 * 11 + 3d) = 56
- Simplifying: 2 * (22 + 3d) = 56
- Therefore, 22 + 3d = 28, which gives 3d = 6, hence d = 2.
Calculating the Sum of the Last Four Terms
- The last four terms can be expressed as:
- Terms: a + (n-4)d, a + (n-3)d, a + (n-2)d, a + (n-1)d
- Sum = 4a + (n-10)d = 112
- Substituting a = 11 and d = 2:
- 4(11) + (n-10)(2) = 112
- 44 + 2n - 20 = 112
- Thus, 2n + 24 = 112, leading to 2n = 88, so n = 44.
Conclusion
- The total number of terms in the AP is 44.
- Sum of the first four terms of an AP is 56.
- Sum of the last four terms of the same AP is 112.
- The first term (a) is 11.
Formulas and Definitions
- The sum of the first n terms of an AP can be calculated using the formula:
Sum = n/2 * (2a + (n-1)d),
where 'a' is the first term, 'd' is the common difference, and 'n' is the number of terms.
Calculating the Sum of the First Four Terms
- For the first four terms:
- n = 4
- Sum = 4/2 * (2 * 11 + 3d) = 56
- Simplifying: 2 * (22 + 3d) = 56
- Therefore, 22 + 3d = 28, which gives 3d = 6, hence d = 2.
Calculating the Sum of the Last Four Terms
- The last four terms can be expressed as:
- Terms: a + (n-4)d, a + (n-3)d, a + (n-2)d, a + (n-1)d
- Sum = 4a + (n-10)d = 112
- Substituting a = 11 and d = 2:
- 4(11) + (n-10)(2) = 112
- 44 + 2n - 20 = 112
- Thus, 2n + 24 = 112, leading to 2n = 88, so n = 44.
Conclusion
- The total number of terms in the AP is 44.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms?
Question Description
Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms?.
Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms?.
Solutions for Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms? defined & explained in the simplest way possible. Besides giving the explanation of
Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms?, a detailed solution for Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms? has been provided alongside types of Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms? theory, EduRev gives you an
ample number of questions to practice Sum of first four terms of an AP is 56 and sum of last four term of an AP is 112 .If thr first term is 11 then find the no. of terms? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup