Two AP's have the same common difference. The difference between their 100th terms is 100. What is the difference between their 1000th terms.
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Two AP's have the same common difference. The difference between their 100th terms is 100. What is the difference between their 1000th terms.
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Answer:
The difference between the 1000th term is also 100.
Explanation:
Let first term of the AP = a
Let first term of the other AP = b
Common difference of both the AP be = d
The 100th term of both the AP:
a + 99d = a100---------------------(Equation - 1)
b + 99d = b100---------------------(Equation - 2)
Subtracting both the Equations:
a100-b100=a-b
Difference of their terms is 100:
a-b=100
Similarly difference between their 1000th terms:
=> a1000 = a+999d
=> b1000 = b+999d
=> a1000 - b1000 = a - b
=> a-b=100
Therefore, the difference between the 1000th term is also 100.