Question

Two arithmetic progressions have the same common difference. The difference between their $100th$ terms is $100,$ what is the difference between their $1000th$ terms

• A. 100
• B. 10000
• C. 100000
• D. 1000

Answer 1

Answer: (A)

100

Let $a$ and $d$ be the first term and common difference of the first AP respectively and $A$ and $d$ be the first term and common difference of the second AP respectively.

Let $a_{100}$ and $A_{100}$ be the ${100}^{th}$ term of the first and second AP respectively.

According to question, $a_{100}-A_{100}=100$

$\Rightarrow (a+99d)-(A+99d)=100$

$\Rightarrow a-A=100$ ...(1)

Now, $a_{1000}-A_{1000}=(a+999d)-(A+999d)=a-A=100$ (from (1))

Hence, the required difference is $100$.