What is the best solution for exercise 5.2 of math in arithmetic progressions of class 10th. It is very important type of question. How i solve easily this question Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?

AnilSinghBoraGuru

# Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms? Q.12

Share

Let, the first term of two APs beÂ

a_{1}Â andÂa_{2}Â respectivelyAnd the common difference of these APs beÂ

d.For the first A.P.,we know,

aÂ =Â_{n}a+(nâˆ’1)dTherefore,a_{100}Â =Âa_{1}+(100âˆ’1)d=Â

a_{1}Â + 99da_{1000}Â =Âa_{1}+(1000âˆ’1)da_{1000}Â =Âa_{1}+999dFor second A.P., we know,

aÂ =Â_{n}a+(nâˆ’1)dTherefore,a_{100}Â =Âa_{2}+(100âˆ’1)d=Â

a_{2}+99da_{1000}Â =Âa_{2}+(1000âˆ’1)d=Â

a_{2}+999dGiven that, difference between 100

^{th}Â term of the two APs = 100Therefore, (

a_{1}+99d) âˆ’ (a_{2}+99d) = 100a_{1}âˆ’a_{2}Â = 100â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..Â(i)Difference between 1000

^{th}Â terms of the two APs(

a_{1}+999d) âˆ’ (a_{2}+999d) =Âa_{1}âˆ’a_{2}From equationÂ

(i),This difference,Â

a_{1}âˆ’a_{2Â }= 100Hence, the difference between 1000

^{th}Â terms of the two A.P. will be 100.