Algebra

Arithmetic Progressions

Finding the Common Difference - Arithmetic Progressions

         

Given the arithmetic progression

10,7,4,1,x,10 ,7, 4, 1, x,

what is xx?

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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?

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Which of the following sequences is NOT an arithmetic progression?

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

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The numbers of red circles in each group in the above diagram form an arithmetic progression. What is the common difference?

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2,a,5,b,8 2, a, 5, b, 8

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

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