Question

Two ap's have same common difference. The difference between their 100th term is 100, what is the difference between their 1000th term?​

Answer 1

U can use the formula an a+(n-1)into d
Take a as 1000 and Das 100 and n as n and a as the first term.
Hope it helps

Answer 2

We know that $a_n=a(n-1)d$.

So, 100th term will be:

$a_{100}=a+(100-1)d$

$a_{100}=a+99d$

So, 100th term of 1st AP = $a+99d$

Let second AP be denoted as:

$b_n=b+(n-1)d$

$b_{100}=b+(100-1)d$

$b_{100}=b+99d$

So, 100th term of 2nd AP = $b+99d$

As per the question,

Difference between their 100th terms = 100

$a_{100}-b_{100}=100$

$(a+99d)-(b+99d)=100$

$a+99d-b-99d=100$

$a-b+99d-99d=100$

$a-b=100$

Now we need to find the difference between 1000th terms.

$=a_{1000}-b_{1000}$

$=[a+(1000-1)d]-[b+(100-1)d]$

$=a+999d-b-999d$

$=a-b+999d-99d$

$=a-b$

Putting value from (1)

$=100$

So, difference between 1000th terms is 100.