Question

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 1

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.