The question is given from NCERT Book of class 10th Chapter no. 5 Ex. 5.2 Q. 12. In the following question you have to find the difference between the 1000th term as said in the above question. Give the solution of the above question.
Deepak BoraNewbie
If two A.P have the same common difference. The difference b/w their 100th term is 100. What is the difference between their 1000th term.
Share
Solution:
Let, the 1st term of two AP’s be a1 and a2 ;
The c.d of the AP’s be ” d ” .
For 1st A.P
an = a+(n−1)d
Therefore,
a100 = a1+(100−1)d
= a1 + 99d
a1000 = a1+(1000−1)d
a1000 = a1+999d
For 2nd A.P ,
an = a+(n−1)d
Therefore,
a100 = a2 + (100−1)d
= a2 + 99d
a1000 = a2 + (1000−1)d
= a2 + 999d
It is given that the difference between 100th term of the two APs = 100
i,e (a1 + 99d) − (a2 + 99d) = 100
a1−a2 = 100 ………………………….. (i)
Diff. b/w 1000th terms of the two APs
(a1+999d) − (a2+999d) = a1−a2
From eq. (i),
This diff. , a1−a2 = 100
The difference between 1000th terms of the 2 A.P’s will be 100.