Question

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

Class 10 - Math - Arithmetic Progressions Page 106

Answer 1

Let two AP's have same commom difference d and Let a and A are the first term of given AP's .
T100 - T'100 = 100
a + (100-1)d -A - (100-1)d = 100
a - A = 100 -----(1)

now,
T1000 - T'1000
= a + (1000-1)d -A - (1000-1)d
= a - A from eqn (1)
= 100

hence, difference between 1000th terms = 100

Answer 2

hopes I helped.....................