Class 10 Exam > Class 10 Questions > The 4 th term of AP is zero, prove that 25th ...
Start Learning for Free
The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term?
Most Upvoted Answer
The 4 th term of AP is zero, prove that 25th term of AP is three times...
Proof: 4th term of AP is zero
Let the AP be represented by a, a + d, a + 2d, a + 3d, .....
Given that the 4th term of the AP is zero.
Therefore, a + 3d = 0
=> a = -3d
Prove that 25th term of AP is three times the 11th term
To prove: 25th term = 3 x 11th term
Method 1: Using the formula for nth term of an AP
The formula for nth term of an AP is given by: a + (n-1)d
Substituting a = -3d and n = 25, we get:
25th term = -3d + 24d = 21d
Substituting a = -3d and n = 11, we get:
11th term = -3d + 10d = 7d
Therefore, 25th term = 3 x 7th term = 21d = 3 x 7d = 3 x 11th term
Method 2: Using the common difference of the AP
We know that the 11th term of the AP is a + 10d and the 25th term of the AP is a + 24d.
Substituting a = -3d, we get:
11th term = -3d + 10d = 7d
25th term = -3d + 24d = 21d
Therefore, 25th term = 3 x 7th term = 21d = 3 x 7d = 3 x 11th term
Hence, we have proved that the 25th term of the AP is three times the 11th term.
Let the AP be represented by a, a + d, a + 2d, a + 3d, .....
Given that the 4th term of the AP is zero.
Therefore, a + 3d = 0
=> a = -3d
Prove that 25th term of AP is three times the 11th term
To prove: 25th term = 3 x 11th term
Method 1: Using the formula for nth term of an AP
The formula for nth term of an AP is given by: a + (n-1)d
Substituting a = -3d and n = 25, we get:
25th term = -3d + 24d = 21d
Substituting a = -3d and n = 11, we get:
11th term = -3d + 10d = 7d
Therefore, 25th term = 3 x 7th term = 21d = 3 x 7d = 3 x 11th term
Method 2: Using the common difference of the AP
We know that the 11th term of the AP is a + 10d and the 25th term of the AP is a + 24d.
Substituting a = -3d, we get:
11th term = -3d + 10d = 7d
25th term = -3d + 24d = 21d
Therefore, 25th term = 3 x 7th term = 21d = 3 x 7d = 3 x 11th term
Hence, we have proved that the 25th term of the AP is three times the 11th term.
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
The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term?
Question Description
The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term? 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 The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term?.
The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term? 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 The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term?.
Solutions for The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term? 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 The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term? defined & explained in the simplest way possible. Besides giving the explanation of
The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term?, a detailed solution for The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term? has been provided alongside types of The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term? theory, EduRev gives you an
ample number of questions to practice The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term? 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup