Question

✔✔Two APs 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

let the two APs be a1,a2,a3,.........an and b1,b2,b3 ........bn .

also let D be the same common difference of two AP then
the nth term of first ap an = a1 + (n-1)d
in the end term of 2nd AP bn = b1 + (n-1 )d

now, an - bn = (a1 + (n-1) d) - (b1 + (n-1)d)
a100 - b100= a1 - b1 =100
a1000 - b1000 = a1 - b1
a1000 - b1000 = 100

hence the difference between their 1000 term is also 100.

I hope it's helpful

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Answer 2

Heya mate
The answer of ur question is





Let the terms of first AP be a,a+d... and terms of second AP be b,b+d......

Given the difference between their 100th terms is 100.

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

a+99d-b-99d=100

a-b=100(eq1)

Now the difference between their 1000th terms is

(a+999d)-(b+999d)

a+999d-b-999d

a-b

But we know a-b=100 from eq1.

So in this case also a-b=100.

Therefore the difference between their 1000th terms is also 100.





hope it helps