What is the best solution for exercise 5.2 of math in arithmetic progressions of class 10th. It is very important type of question. How i solve easily this question Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?
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Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms? Q.12
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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.