Question

2ap s have the same common difference . the difference between their 1ooth term is 100 what is the difference between their 1000th terms
​

Answer 1

Answer:

a-b=100

Step-by-step explanation:

Difference between their 1000th terms will be the same

Let 2 APs be as follows… ( Their common difference is 'd' )

a , a+d, a+2d, a+3d,………….

b, b+d, b+2d, b+3d,……….

Difference between their 100th terms

(a+99d) - (b+ 99d) = 100 ( by given condition)

=> a - b = 100

Now, difference between their 1000th terms

(a + 999d) - (b + 999d) = ?

= a + 999d - b - 999d

= a - b= 100

Answer 2

Answer:

$100$

Step-by-step explanation:

Given that 2 ap's have same common difference

given that their 100th terms difference is 100

let the first no. of first series be a1 and second series be a2

then, a(1)100-a(2)100 100 1

for 1st series ---- a100-a1+99d

2nd series ---- a100 = a2+99d

keep these values in (1)

then,

a1+99d-(a2+99d) = 100 a1+99d-a2-99d=100

therefore, a1-a2 =100

2 then the difference between their 1000th terms is

for 1st series -- a1000 = a1+999d

for 2nd series --- a1000 = a2+999d

their 100th terms difference is

a(1)1000-a(2)1000

a1+999d-(a2+999d)

a1+999d-a2-999d

therefore we get the value a1-a2

from (2) a1-a2 = 100

therefore the difference between their 1000th terms is 100.