Question

two APs have the same common difference. if the difference between their 200th terms is 222444888 then the difference between their 200000th terms is
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Answer 1

Given : Two APs have the same common difference. if the difference between their 200th terms is 222444888

To find : let common difference of each AP is d and first term of 1st ap is A and 2nd ap is a.

200th term of 1st ap, T₂₀₀ = A + (200 - 1)d = A + 199d

200th term of 2nd ap, t₂₀₀ = a + (200 - 1)d = a + 199d

as, T₂₀₀ - t₂₀₀ = 222444888

⇒ A + 199d - a - 199d = (A - a) = 222444888......(1)

now 200000th term of 1st ap, T₂₀₀₀₀₀ = A + (200000 - 1) = A + 199999d

200000th term of 2nd ap, t₂₀₀₀₀₀ = a + (200000 - 1)r = a + 199999d

so, T₂₀₀₀₀₀ - t₂₀₀₀₀₀ = A + 199999d - a - 199999d

= A - a = 222444888 [ from equation (1). ]

Therefore the difference between their 200000th terms is 222444888.