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?

• A. 1000
• B. 100
• C. 150
• D. 200

Answer 1

The correct option is B

100

Let first term of $1^{st}$ AP = a

Let first term of $2^{nd}$ AP = a'

It is given that their common difference is same. Let their common difference be d.

It is given that difference between their ${100}^{th}$ terms is 100.
Using formula $a_n$ = a + (n−1) d, to find $n^{th}$ term of arithmetic progression, we can say that

$[a+(100-1\left)d\right]-[a^{\prime }+(100-1\left)d\right]=100\Rightarrow a+99d-a^{\prime }-99d=100$

$\Rightarrow a-a^{\prime }=100$ ........ (1)

We want to find difference between their ${1000}^{th}$ terms which means we want to calculate:

$a+(1000-1)d-(a^{\prime }+(1000-1\left)d\right)=a+999d-a^{\prime }-999d=a-a^{\prime }$
$=100$ .........from(1)

$\therefore$ Difference between their 1000${}^{th}$ terms would be equal to 100.