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Arithmetic Progressions

What's the sum of the first 100 positive integers? How about the first 1000? Learn the fun and fast way to solve problems like this. See more

Common Difference

         

Given the arithmetic progression

\[10 ,7, 4, 1, x,\]

what is \(x\)?

My doctor gave me some pills with the following instructions:

"Take 12 pills on the first day, and then reduce the amount by 3 pills on each subsequent day until you don't have to take any."

When will be the first day that I don't have to take any pills?

Which of the following sequences is NOT an arithmetic progression?

(A) \( \{ 11, 5, -1, -7, -13, \cdots \} \)
(B) \( \{ 5, 5, 5, 5, 5, \cdots \} \)
(C) \( \{ 1, 2, 4, 6, 8, \cdots \} \)

The number of red circles in each group of the above diagram forms an arithmetic progression. What is its common difference?

\[ 2, a, 5, b, 8 \]

If the above numbers form an arithmetic progression, what is its common difference?

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