Question

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

Answer 1

Here's the solution, hope it helps you!

Answer 2

To Find :

• we need to find the difference between 1000 th term if the two AP's have same common difference.

Given :

• Two AP's have same common difference .
• Difference between their 100th term is 100.

Let the common difference be d and first term of 1st AP be a and First term of 2nd AP be a2.

Now

As we know that,

• an = a + (n - 1)d

100th term of 1st AP :-

= a + (100 - 1)d

= a + 99d.

100th term of 2nd AP is a2 + 99d

As it is given in the Question that difference between their 100th term is 100

So,

➔ a + 99d -(a2 + 99d) = 100

➔ a + 99d - a2 - 99d = 100

➔ a - a2 = 100 .........1)

Now,

Finding difference between their 1000th term

• 1000th term of 1st AP = a + 999d
• 1000th term of 2nd AP = a2 + 999d

So,

➔ a + 999d - (a2 + 999d)

➔ a + 999d - a2 - 999d

➔ a - a2

From equation...1)

› a - a2 = 100

So,

Difference between their 1000th term is 100 .

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