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The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term?
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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.
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The 4 th term of AP is zero, prove that 25th term of AP is three times the 11th term?
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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?.
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