Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?
Let, the first term of two APs be a1 and a2 respectively
And the common difference of these APs be d.
For the first A.P., we know,
an = a+(n−1)d
a100 = a1+(100−1)d
= a1 + 99d
a1000 = a1+(1000−1)d
a1000 = a1+999d
For second A.P., we know,
an = a+(n−1)d
Therefore,
a100 = a2+(100−1)d
= a2+99d
a1000 = a2+(1000−1)d
= a2+999d
Given that, difference between 100th term of the two APs = 100
Therefore, (a1+99d) − (a2+99d) = 100
a1−a2 = 100 ……………….. (i)
Difference between 1000th terms of the two APs
(a1+999d) − (a2+999d) = a1−a2
From equation (i),
This difference, a1−a2 = 100
Hence, the difference between 1000th terms of the two A.P. will be 100.