# Two arithmetic pr

Two arithmetic progressions have the same common difference.

Let, common difference = d

First term of first A.P. = a

First term of second A.P. = a’

Given that difference between their 100th term is 100

100th term of first A.P., a100 = a + 99d

100th term of second A.P., a’100 = a’ + 99d

Acc. To question,

a100 – a’100 = 100

a + 99d – a’ – 99d = 100

a – a’ = 100 (i)

1000th term of first A.P., a1000 = a + 999d

1000th term of second A.P., a’1000 = a’ + 999d

Acc. To question,

a1000 – a’1000 = a + 999d – a’ – 999d

= a – a’

a1000 – a’1000 = 100 [from (i)]

Hence, difference between 1000th term of two A.P. is 100

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