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) \( \{ 1, 2, 4, 6, 8, \cdots \} \)
The numbers of red circles in each group in the above diagram form an arithmetic progression. What is the common difference?
\[ 2, a, 5, b, 8 \]
If the above numbers form an arithmetic progression, what is its common difference?