Let the common difference of two AP's be d, their first terms as a and a'nth term of both the AP's will be given byan = a + (n - 1) da'n = a' + (n - 1) dNow 100th term of 1st AP will be given by: a100 = a + (100 - 1) d = a + 99d100th term of second AP will be given by: a'100 = a' + (100 - 1) d = a' + 99dGiven, a100 - a'100 = (a + 99 d) - (a' + 99 d)⇒a100 - a'100 = (a - a')So, difference does not depend on number of terms.Thus, a1000 - a'1000 = 100 = a100-a'100So the difference between their 1000th terms is 100.

Q. 123.7( 319 Votes )

Two APs have the

Class 10th NCERT - Mathematics 5. Arithmetic Progressions

Answer :

Let the common difference of two AP's be d, their first terms as a and a'
nth term of both the AP's will be given by
a_n= a + (n - 1) d
a'_n= a' + (n - 1) d
Now 100th term of 1st AP will be given by: a₁₀₀ = a + (100 - 1) d = a + 99d
100th term of second AP will be given by: a'₁₀₀ = a' + (100 - 1) d = a' + 99d
Given, a₁₀₀- a'₁₀₀= (a + 99 d) - (a' + 99 d)
⇒a₁₀₀- a'₁₀₀= (a - a')
So, difference does not depend on number of terms.
Thus, a₁₀₀₀- a'₁₀₀₀= 100 = a₁₀₀-a'₁₀₀So the difference between their 1000th terms is 100.