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Question
Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?
Solution
Let for the 1st AP, the first term = a and common difference = d
T100 = a + 99d
And for the 2nd AP, the first term = a and common difference = d
T100 = a + 99d
According to the condition
T100 - T100 = 100
a + 99d - (a + 99d) = 100
a - a = 100
Let T1000 - T1000 = x
a + 999d - (a + 999d) = x
a - a = x
x = 100
The difference between the 1000th terms is 100.
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