There are a lot of problems here so I'll try to be brief with each one so I don't add a lot of clutter
Problem 10) This is <u>arithmetic</u> because we subtract 6 from each term to get the next. This is the same as adding on -6. The common difference is d = -6. The first term is a = 1
Problem 11) <u>Neither</u>. The distance from 3 to 3/2 = 1.5 is 1.5 units, but the distance from 1.5 to 1 is 0.5 units. This implies there is no common difference value. The sequence is not arithmetic because of this. It's also not geometric either. To go from 3 to 3/2, we multiply by 1/2. But then going from 3/2 to 1, we multiply by 2/3. There is no common ratio r value.
Problem 12) This sequence is <u>geometric</u>. We divide each term by 3 to get the next, or put another way, we multiply each term by 1/3 to get the next term. The common ratio is r = 1/3. The first term is a = 108.
Problem 13) <u>Neither</u>. This is because going from term to term, we do not add the same amount each time. Example: from -2 to 4 we add 6, but then from 4 to -6 we add -10. So the sequence is not arithmetic. It's also not geometric either because we dont multiply by the same term each time. Eg: from -2 to 4, we multiply by -2; but from 4 to -6 we multiply by -1.5
Problem 14) The next three terms are: <u>1, 1/4, 1/16</u>. This is found by multiplying each term by the common ratio r = 1/4, or you can think of dividing each term by 4. To get this common ratio, pick any term you want and divide it by its previous term. Example: term2/term1 = 16/64 = 1/4 = common ratio.
Problem 15) The next three terms are: <u>-432, 2592, -15552</u>. You multiply each term by the common ratio -6. Like with the previous problem, we divide any term over its previous one to get the common ratio, so for example, term2/term1 = -12/2 = -6 = common ratio.
