Identify the sequence 2 2 2 2 as arithmetic or geometric Th

Identify the sequence {-2, 2, -2, 2 ...} as arithmetic or geometric. Then find the common difference or ratio as appropriate. Show all work.

Solution

An arithmetic sequence goes from one term to the next by always adding (or subtracting) the same value. For instance, 2, 5, 8, 11, 14,... and 7, 3, –1, –5,... are arithmetic, since you add 3 and subtract 4, respectively, at each step. A geometric sequence goes from one term to the next by always multiplying (or dividing) by the same value. So 1, 2, 4, 8, 16,... and 81, 27, 9, 3, 1, 1/3,... are geometric, since you multiply by 2 and divide by 3, respectively, at each step.\"

According to this, let\'s see the sequence:
-2, 2, -2, 2...

LEt\'s try to calculate the common difference:
2 - (-2) = +4
-2 - 2 = -4
2-(-2) = +4

The common difference is 4, but is also -4. This is not apropiate to an arithmetic or geometric sequence, but if they have a common ratio then, we can say if this is arithmetic or geometric

The ratio is the same:
-2/2 = -1
2/-2 = -1
-2/2 = -1

So, this means that in order to get the next number, we multiply by -1 to get the other. So we can conclude this sequence is geometric

Hope this helps