Question

two APs have same common difference . the difference between their 100th term is 100 , what is the difference between their 1000th term......
plz.. solve it...

Answer 1

let first term =a let first term =b
common difference=d common diff=d

a100= a+99d
b100= b+99d
a100-b100=a-b
a-b=100
a1000=a+999d
b1000=b+999d
a1000-b1000 =a-b
a-b=100
so the common difference is 100 answer

Answer 2

Answer:

The difference between their 1000th term is also 100

Step-by-step explanation:

Given that two APs have same common difference . the difference between their 100th term is 100,

we have to find the difference between their 1000th term.

Let the first term of one AP is a

Let the first term of other A.P is b

As given common difference of two A.P series is same let it be d

The 100th term of both A.P is

$a_{100}= a+99d$   →   (1)

$b_{100}= b+99d$   →   (2)

Subtracting (2) from (1)

$a_{100}-b_{100}=a-b$

As difference between their 100th term is 100

$a-b=100$

$a_{1000}=a+999d$

$b_{1000}=b+999d$

$a_{1000}-b_{1000} =a-b$

$a-b=100$

Hence, the difference between their 1000th term is also 100