Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms. Why
Solution:
An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. It is obtained by adding the same fixed number to its previous term.
Let the same common difference between two AP’s is d.
From the question given,
The first term of first AP (a₁) = 2
The first term of second AP(a₂) = 7
The AP’s are
2, 2 + d, 2 + 2d, 2 + 3d ….
7, 7 + d, 7 + 2d, 7 + 3d ….
The 10th term of the first AP is 2 + 9d
The 10th term of the second AP is 7 + 9d.
aₙ = a + (n - 1)d.
a₁₀ = a + (10 - 1 )d
Their difference is 7 + 9d - (2 + 9d) = 5
The 21st term of the first AP is 2 + 20d.
The 21st term of the second AP is 7 + 20d.
aₙ = a + (n - 1)d.
a₂₁ = a + (21 - 1 )d
Their difference is 7 + 20d - (2 + 20d) = 5
If,
the aₙ and bₙ are nth terms of first and second AP,
Then,
bₙ - aₙ = [7 + (n - 1 )d)] - [2 + (n - 1)d] = 5
Therefore, the difference between any two corresponding terms of such AP’s is the same as the difference between their first terms.
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☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.2 Problem 4
Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms. Why
Summary:
Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms,the difference between any two corresponding terms of such AP’s is the same as the difference between their first terms
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