Question

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

Answer 1

Step-by-step explanation:

Given that,

common difference are equal of both APs

Let the first term of first AP be 'x'

first term of secondAP be 'y'

x+99d-(y+99d)=100(given)

x+99d-y-99d=100

x-y=100(eq1)

so,x+999d-(y+999d)=x+999d-y-999d

=x-y

=100(by eq1)

therefore difference will be 100

mark me as brainlist.

Answer 2

The difference between their 1000th terms is 100

Given :

• 2 AP's have same common difference.
• Their 100th terms difference is 100.

To Find :

The difference between their 1000th term.

Solution:

Consider the :

The first number of first series as - x1 & Second series as x2

Then,

→ x(1)100 - x(2)100 = 100

____________[ Equation 1 ]

• 1st Series : x100=x1 + 99d
• 2nd series : x100 = x2 + 99d

Values in Equation 1,

So,

→ x1 + 99d - (x2 + 99d) = 100

→ x1 + 99d - x2 - 99d = 100

•°• x1 - x2 = 100

____________[ Equation 2 ]

So, the difference between their 1000th terms :

1st series : x1000 = x + 999d

2nd series : x1000 = x2+ 999d

Their 100th terms difference,

→ x(1)1000 - x(2)1000

→ x1+999d - (x2 + 999d)

→ x1+999d - x2 - 999d

So,

The value we get from (2) x1 - x2 = 100 is x1 - x2

Hence,

The difference between their 1000th terms is 100.