Which of the following sequences of numbers are arithmetic sequences? Check all that apply. A. 45, 46, 47, 48, 49, ... B. 54, 71, 88, 105, 122, ... C. 3, 10, 17, 24, 31, ... D. 1, -2, 3, -4, 5, ... E. -3, -11, -17, -23, -33, ...

Question

Which of the following sequences of numbers are arithmetic sequences?   Check all that apply.   		A.	45, 46, 47, 48, 49, ...  		B.	54, 71, 88, 105, 122, ...  		C.	3, 10, 17, 24, 31, ...  		D.	1, -2, 3, -4, 5, ...  		E.	-3, -11, -17, -23, -33, ...

texaschic101 · Answer

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.....that means the difference between all the numbers is the same.
Lets try a couple...

A. 45,46,47,48,49....the difference between each number is 1...it is a constant difference. therefore, this IS an arithmetic sequence.
B. 54,71,88,105,122....71 - 54 = 17, 88 - 71 = 17,105 - 88 = 17,122-105 = 17....as you can see, the difference between all the numbers is 17. So, this IS an arithmetic sequence.

Just remember, if the difference between all the numbers is the same, then it is an arithmetic sequence. If the difference between all the numbers is not the same, then it is not an arithmetic sequence.

Now see what you can do with C,D, and E :)