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प्रश्न
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?
उत्तर
Suppose there are two AP’s with first terms a and A
And their common differences are d and D respectively
Suppose n be any term
an = a + (n – 1)d
An = A + (n – 1)D
As common difference is equal for both AP’s
We have D = d
Using this we have
An – an = a + (n – 1)d – [A + (n – 1)D]
= a + (n – 1)d – A – (n – 1)d
= a – A
As a – A is a constant value
Therefore, difference between any corresponding terms will be equal to a – A.
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