Question

Two AP's have the same common difference. The difference between their ${100}^{th}$ terms is 100, what is the difference between their ${1000}^{th}$ terms?

Answer 1

$a_n=a+\left(n-1\right)d$

100^th term will be,

$a_{100}=a+\left(100-1\right)d$

$a_{100}=a+99d$

100^th term of 1^st Ap = a + 99d

2^nd AP will be,

$b_n=b_n+\left(n-1\right)d$

$b_{100}=b+99d$

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

$\left(a+99d\right)-\left(b+99d\right)=100$

$a-b=100...\left(1\right)$

Difference between 1000^th term,

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

$=a+\left(1000-1\right)d)-\left[b+\left(1000-1\right)d\right]$

$=a-b+999d-999d$

$=100$