Algebra
# Arithmetic Progressions

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) \( \{ 1, 2, 4, 6, 8, \cdots \} \)

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

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