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12. Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?

12. Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
2 years ago
Let, the first term of two APs be a1 and a2 respectively And the common difference of these APs be d. For the first A.P.,we know, an = a+(n−1)d Therefore, a100 = a1+(100−1)d = a1 + 99d a1000 = a1+(1000−1)d a1000 = a1+999d For second A.P., we know, an = a+(n−1)d Therefore, a100 = a2+(100−1)d = a2+99d a1000 = a2+(1000−1)d = a2+999d Given that, difference between 100th term of the two APs = 100 Therefore, (a1+99d) − (a2+99d) = 100 a1−a2 = 100……………………………………………………………….. (i) Difference between 1000th terms of the two APs (a1+999d) − (a2+999d) = a1−a2 From equation (i), This difference, a1−a2 = 100 Hence, the difference between 1000th terms of the two A.P. will be 100.

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