Two AP have the same common difference. The difference between their

1.	Two AP have the same common difference. The difference between their 100th terms is 100. what is the difference between their 1 000th terms?
Answer» Having common difference ‘d’, the AP 1st set a, a+d, a+2d 2nd set b, b + d, b + 2d 100^th term of 1st set – 100^th term of 2nd set = 100 ∴ a + 99d – (b + 99d) = 100 a + 99d – b – 99d = 100 a – b= 100 Similarly. 1000th term of 1st set = 1 + 999d 1000 th term of 2nd set = b + 999d Their difference = a + 999d – (b + 999d) = a + 999d – b – 999d = a – b.

Two AP have the same common difference. The difference between their 100th terms is 100. what is the difference between their 1 000th terms?

Answer»

Having common difference ‘d’, the AP

1st set a, a+d, a+2d

2nd set b, b + d, b + 2d

100^th term of 1st set – 100^th term of 2nd set = 100

∴ a + 99d – (b + 99d) = 100

a + 99d – b – 99d = 100 a – b= 100

Similarly.

1000th term of 1st set = 1 + 999d

1000 th term of 2nd set = b + 999d

Their difference

= a + 999d – (b + 999d)

= a + 999d – b – 999d

= a – b.