Question

Which of the following sequences of numbers are arithmetic sequences?

Check all that apply.

A. 8, 10.5, 13, 15.5, 18, ...
B. 1001, 1001, 1002, 1003, 1004, ...
C. 3, -3, 3, -3, 3, ...
D. -5, -8, -11, -14, -17, ...
E. 0, 5, 10, 15, 20, ...

Answer 1

Arithmetic sequence are those that have a common difference

Common difference, ususally denoted by d, is the same number being ADDED or SUBTRSCTED (addition/subtraction is important bc this seperates it from a geometric sequence)

Anyways the subtracted part really means it's adding a negative each time so you can say subtracted. Anyways, what you do is take a number and subtract it from the preceeding number and then you continue on and if you keep getting the same "common differece"then it's an arithmetic sequence.

Whether you understood that or not, I'l do A for you

10.5 (2nd number)-8 (1st number)=2.5
13 (3rd number)-10.5 (2nd number)=2.5 (There's a pattern of 2.5 going on)
15.5 (4th number)-13( 3rd number)=2.5
18-15.5=2.5

The "common differene"between all those numbers is 2.5 so A is an arithmetic seuqence