UPSC Exam > UPSC Questions > In an A.P, the 12th term is 7 times the 2nd t...
Start Learning for Free
In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.
- a)152
- b)144
- c)156
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3...
Let the progression be a,a+d,a+2d..................
The 1st line gives us the equation, a+lld=7a+7d = 6a=4d
= 3a=2d------------------ (1)
Also, a+7d = 10a+3 = 7d=9a+3
= 7d=6d+3 from (1), we get 3a=2d, hence 9a = 6d
^ d=3,a=2
The GP is 2,2x3,2x32,2x33,2x34.
So the 5th term is 162. Hence, d.
Most Upvoted Answer
In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3...
To solve this problem, we need to find the common difference of the arithmetic progression (AP) and then use it to find the common ratio of the geometric progression (GP).
Let's start by defining the AP. We are given that the 12th term is 7 times the 2nd term, which can be written as:
a + 11d = 7(a + d)
Simplifying this equation, we get:
a + 11d = 7a + 7d
4a = 4d
a = d
So, the common difference of the AP is equal to the first term, a.
Next, we are given that the 8th term is 3 more than 10 times the first term, which can be written as:
a + 7d = 10a + 3
Simplifying this equation, we get:
7d = 9a + 3
7d - 3 = 9a
7(a) - 3 = 9a
3 = 2a
a = 3/2
So, the first term of the AP is 3/2 and the common difference is also 3/2.
Now, let's move on to finding the common ratio of the GP. The common ratio of a GP can be found by dividing any term by its preceding term. In this case, we will divide the 5th term by the 4th term.
The 4th term of the AP can be found by substituting n = 4 into the AP formula:
a + (4-1)d = a + 3d
3/2 + 3/2 = 3
The 5th term of the AP can be found by substituting n = 5 into the AP formula:
a + (5-1)d = a + 4d
3/2 + 4(3/2) = 9
Therefore, the common ratio of the GP is:
9/3 = 3
So, the first term of the GP is 3/2 and the common ratio is 3. To find the 5th term of the GP, we can use the formula for the nth term of a GP:
Tn = ar^(n-1)
Substituting the values, we get:
T5 = (3/2)(3)^(5-1)
T5 = (3/2)(3)^4
T5 = (3/2)(81)
T5 = 243/2
Therefore, the 5th term of the GP is 243/2.
Since none of the given options match with 243/2, the correct answer is option 'D', None of these.
Let's start by defining the AP. We are given that the 12th term is 7 times the 2nd term, which can be written as:
a + 11d = 7(a + d)
Simplifying this equation, we get:
a + 11d = 7a + 7d
4a = 4d
a = d
So, the common difference of the AP is equal to the first term, a.
Next, we are given that the 8th term is 3 more than 10 times the first term, which can be written as:
a + 7d = 10a + 3
Simplifying this equation, we get:
7d = 9a + 3
7d - 3 = 9a
7(a) - 3 = 9a
3 = 2a
a = 3/2
So, the first term of the AP is 3/2 and the common difference is also 3/2.
Now, let's move on to finding the common ratio of the GP. The common ratio of a GP can be found by dividing any term by its preceding term. In this case, we will divide the 5th term by the 4th term.
The 4th term of the AP can be found by substituting n = 4 into the AP formula:
a + (4-1)d = a + 3d
3/2 + 3/2 = 3
The 5th term of the AP can be found by substituting n = 5 into the AP formula:
a + (5-1)d = a + 4d
3/2 + 4(3/2) = 9
Therefore, the common ratio of the GP is:
9/3 = 3
So, the first term of the GP is 3/2 and the common ratio is 3. To find the 5th term of the GP, we can use the formula for the nth term of a GP:
Tn = ar^(n-1)
Substituting the values, we get:
T5 = (3/2)(3)^(5-1)
T5 = (3/2)(3)^4
T5 = (3/2)(81)
T5 = 243/2
Therefore, the 5th term of the GP is 243/2.
Since none of the given options match with 243/2, the correct answer is option 'D', None of these.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.a)152b)144c)156d)None of theseCorrect answer is option 'D'. Can you explain this answer?
Question Description
In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.a)152b)144c)156d)None of theseCorrect answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.a)152b)144c)156d)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.a)152b)144c)156d)None of theseCorrect answer is option 'D'. Can you explain this answer?.
In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.a)152b)144c)156d)None of theseCorrect answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.a)152b)144c)156d)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.a)152b)144c)156d)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.a)152b)144c)156d)None of theseCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.a)152b)144c)156d)None of theseCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.a)152b)144c)156d)None of theseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.a)152b)144c)156d)None of theseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.a)152b)144c)156d)None of theseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In an A.P, the 12th term is 7 times the 2nd term and the 8th term is 3 more than 10 times the first term. What is the 5th term of the G.P whose first term is the first term of A.P and whose common ratio is equal to the common difference of the A.P.a)152b)144c)156d)None of theseCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
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