Two APs have the same common difference. The first term of one AP is 2

1.	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.
Answer» Let a, d and a_n be the first term, common difference and nth term of first AP and A, d and A_n be the first term, common difference and nth term of second AP respectively. Given a=2 and A=7 Also, given that, a₁₀−A₁₀=a + 9d − (A + 9d )= a − A = 2 − 7 = −5 and a₂₁ − A₂₁= a + 20d −(A + 20d) = a − A = 2 − 7 = −5 Hence, the difference between any two corresponding terms of these AP's is equal to difference between first terms of these AP's. ∴ given statement is true so answer is 1.

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.

Answer»

Let a, d and a_n be the first term, common difference and nth term of first AP and

A, d and A_n be the first term, common difference and nth term of second AP respectively.

Given a=2 and A=7

Also, given that, a₁₀−A₁₀=a + 9d − (A + 9d )= a − A = 2 − 7 = −5

and a₂₁ − A₂₁= a + 20d −(A + 20d) = a − A = 2 − 7 = −5

Hence, the difference between any two corresponding terms of these AP's is equal to difference between first terms of these AP's.

∴ given statement is true so answer is 1.

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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.

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