Question

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

Answer 1

Answer:

100

Step-by-step explanation:

Let the common difference of both the APs be d and d' respectively. And the first terms be a and A respectively.

ATQ,

d = d' ....... equation 1

Also it's given that,

a100 - A100 = 100

{a + (n - 1 ) d} - {A + (n - 1) d'} = 100

[since an = a + (n - 1 ) d]

{a + (100 - 1) d} - {A + (100 - 1) d'} = 100

a + 99d - A - 99d' =100. (from 1)

a - A = 100 ........equation 2

now,

a 1000 - A1000

a + (n-1)d - { A + (n-1) d'}

a + (1000 - 1)d -{A + (1000-1) d'}

a + 999d - { A + 999d'}

a + 999d - A - 999d'

a - A (from 1)

100. (from2)

Hope it helps