1) Geometric series.
You can see that dividing each term by its preceding term, will be a constant.
For instance second term divided by the first term is 2/1=2 third term divided by the second is 4/2=2
fourth term divided by the third is 8/4=2 and so forth.
2) Neither.
Please look at the answers for parts a,c,d and you will see why this is neither. There is no constant that if you add it to any term you get the next term or if you multiply it by any term you get the next term. So it is neither.
3) Geometric series.
Same reasoning as part a. You can easily see that if you multiple each term by a constant, you will get the next term. So 3*-2=6, and -6*-2= 12 and so forth. This is same as saying if you divide each term by it's preceding term you will get a constant (which is -2).
4) Arithmetic Series.
each term in an arithmetic series is equal to the preceding term plus a constant. In other words, the difference between each term and its preceding term is a constant. You can see that the second term minus the first is 8-4=4. The third minus the second is 12-8=4, and so forth.
