Arithmetically different

Algebra Level 2

Two arithmetic progressions have the same common difference. The difference between their 100th terms is 100. What is the difference between their 1000th term?

The answer is 100.

2 solutions

Nihar Mahajan
Feb 12, 2015

Let $<P>$ be an $A.P$ with first term $a$ common difference $d$ .

$So , P_{100} = a + 99d$

Let $<Q>$ be an $A.P$ with first term $b$ common difference $d$ .

$So , Q_{100} = b + 99d$

Thus , $P_{100} - Q_{100} = a - b = 100$

Since their common difference $d$ is same ,

$P_i - Q_i = a - b$ and remains constant as $(i - 1)d$ gets cancelled and it becomes independent of the varying nature of $i$

Hence , $P_{1000} - Q_{1000} = a - b = 100$

Moderator note:

Yes correct! You could have saved the step by not expressing $P_{100}$ and $Q_{100}$ in terms of $a$ and $d$ .

LOL, Do you post solutions everywhere? btw, Easy question. Well done xD

Mehul Arora - 6 years, 1 month ago

Yeah I post everywhere! xD Upvote if satisfied! Cheers!

Nihar Mahajan - 6 years, 1 month ago

Noel Lo
Apr 21, 2015

Nice trick question!!!

Arithmetically different

The answer is 100.

2 solutions

Moderator note:

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