Please help me

kpinky · **Joined:** Tue, 3 Apr 2012 08:08:57 UTC **Posts:** 4

I have a problem.. Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms? I have difficulty in understanding the problem..it has lenghty explaination http://www.youtube.com/watch?v=pCKliUm03wk do you have other method of solving this question

Soroban · **Posted:** Tue, 3 Apr 2012 14:32:22 UTC

Hello, kpinky!

Quote:

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

We have two arithmetic progressions with the same common difference:

. . $\begin{Bmatrix}a_n &=& a_{_1} + (n-1)d \\ b_n &=& b_{_1} + (n-1)d \end{Bmatrix}$

Their 100th terms differ by 100: . $a_{_{100}} - b_{_{100}} \:=\:100$

. . $(a_{_1} + 99d) - (b_{_1} + 99d) \:=\:100 \quad\Rightarrow\quad a_{_1} - b_{_1} \:=\:100$

That is, their first terms differ by 100.

Therefore, their 1000th terms also differ by 100.

S.O.S. Mathematics CyberBoard

Please help me

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