CA Foundation Exam > CA Foundation Questions > The sum of a certain number of terms of an AP...
Start Learning for Free
The sum of a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms is
- a)12
- b)13
- c)11
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The sum of a certain number of terms of an AP series –8, –...
Let the number of terms is N.
Given,
First term ( a ) = -8
Common difference ( d ) = Difference of two consecutive terms
= ( -6 ) - ( -8 ) = -6 + 8 = 2.
Now,
⇒ Sum of N terms of an A.P. = N/2 { 2 a + ( N - 1 ) d }
⇒ 52 = N/2 { 2 x ( -8 ) + ( N - 1 )2 }
⇒ 52 = N/2 { -16 + 2N - 2 }
⇒ 52 = N/2 ( -18 + 2N )
⇒ 52 x 2 = N ( -18 + 2N )
⇒ 104 = -18N + 2N^2
⇒ 104 = 2 ( -9N + N^2 )
⇒ 104/2 = -9N + N^2
⇒ 52 = -9N + N^2
⇒ 0 = N^2 - 9N - 52
⇒ 0 = N^2 - 13N + 4N - 52
⇒ 0 = N ( N - 13 ) + 4 ( N - 13 )
⇒ 0 = ( N - 13 ) ( N + 4 )
∴ N = either 13 or -4.
But the numbers of terms in an A.P. can't be negative.
Therefore, the possible value is 13.
Most Upvoted Answer
The sum of a certain number of terms of an AP series –8, –...
Free Test
FREE
| Start Free Test |
Community Answer
The sum of a certain number of terms of an AP series –8, –...
Given: AP series 8, 6, 4 and sum of certain number of terms is 52
To find: Number of terms in AP series
Approach:
Let the first term of AP be 'a' and common difference be 'd'
Sum of n terms of AP formula: Sn = n/2 [2a + (n-1)d]
Given, Sn = 52
Substituting a=8 and d=-2 in the formula: 52 = n/2 [16 - 2n + 2]
Simplifying the equation, we get 2n² - 26n + 72 = 0
Solving the quadratic equation using the formula (-b ± sqrt(b²-4ac))/2a, we get n=6, 12
As the number of terms in the series is positive, we can neglect n=6
Therefore, the number of terms in the AP series is 12
Answer: Option (B) 13
To find: Number of terms in AP series
Approach:
Let the first term of AP be 'a' and common difference be 'd'
Sum of n terms of AP formula: Sn = n/2 [2a + (n-1)d]
Given, Sn = 52
Substituting a=8 and d=-2 in the formula: 52 = n/2 [16 - 2n + 2]
Simplifying the equation, we get 2n² - 26n + 72 = 0
Solving the quadratic equation using the formula (-b ± sqrt(b²-4ac))/2a, we get n=6, 12
As the number of terms in the series is positive, we can neglect n=6
Therefore, the number of terms in the AP series is 12
Answer: Option (B) 13
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
The sum of a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms isa)12b)13c)11d)None of theseCorrect answer is option 'B'. Can you explain this answer?
Question Description
The sum of a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms isa)12b)13c)11d)None of theseCorrect answer is option 'B'. Can you explain this answer? 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 a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms isa)12b)13c)11d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms isa)12b)13c)11d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
The sum of a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms isa)12b)13c)11d)None of theseCorrect answer is option 'B'. Can you explain this answer? 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 a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms isa)12b)13c)11d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms isa)12b)13c)11d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The sum of a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms isa)12b)13c)11d)None of theseCorrect answer is option 'B'. Can you explain this answer? 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 a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms isa)12b)13c)11d)None of theseCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The sum of a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms isa)12b)13c)11d)None of theseCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The sum of a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms isa)12b)13c)11d)None of theseCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The sum of a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms isa)12b)13c)11d)None of theseCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The sum of a certain number of terms of an AP series –8, –6, –4,…… is 52. The number of terms isa)12b)13c)11d)None of theseCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation 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