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The first and the last terms of an AP are a and l respectively. Show that the sum of the nth term from the beginning and the nth term from the end is (a+l).?
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The first and the last terms of an AP are a and l respectively. Show t...
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The first and the last terms of an AP are a and l respectively. Show t...
Introduction:
In this problem, we are given the first term (a) and the last term (l) of an arithmetic progression (AP). We need to prove that the sum of the nth term from the beginning and the nth term from the end is equal to the product of the first and last terms of the AP, i.e., (a * l).
Proof:
Let's consider the AP: a, a+d, a+2d, ..., l
Where a is the first term, d is the common difference, and l is the last term.
Step 1: Finding the nth term from the beginning
The nth term from the beginning can be represented as a + (n-1)d. This is because the first term is a, and each subsequent term is obtained by adding the common difference d.
Step 2: Finding the nth term from the end
The nth term from the end can be determined by subtracting (n-1)d from the last term l. This can be represented as l - (n-1)d.
Step 3: Sum of the nth term from the beginning and the nth term from the end
The sum of the nth term from the beginning and the nth term from the end can be calculated as follows:
(a + (n-1)d) + (l - (n-1)d)
On simplifying, we get:
a + l - (n-1)d + (n-1)d
a + l
Conclusion:
From the above steps, we can conclude that the sum of the nth term from the beginning and the nth term from the end is equal to the product of the first and last terms of the arithmetic progression, i.e., (a * l).
Therefore, the statement has been proven.
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The first and the last terms of an AP are a and l respectively. Show that the sum of the nth term from the beginning and the nth term from the end is (a+l).?
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The first and the last terms of an AP are a and l respectively. Show that the sum of the nth term from the beginning and the nth term from the end is (a+l).? 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 first and the last terms of an AP are a and l respectively. Show that the sum of the nth term from the beginning and the nth term from the end is (a+l).? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The first and the last terms of an AP are a and l respectively. Show that the sum of the nth term from the beginning and the nth term from the end is (a+l).?.
The first and the last terms of an AP are a and l respectively. Show that the sum of the nth term from the beginning and the nth term from the end is (a+l).? 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 first and the last terms of an AP are a and l respectively. Show that the sum of the nth term from the beginning and the nth term from the end is (a+l).? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The first and the last terms of an AP are a and l respectively. Show that the sum of the nth term from the beginning and the nth term from the end is (a+l).?.
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