Hey please help me solve my assignment I was absent last meeting please. I would appreciate you guys helping me thanks 🥺
Instruction: Write geometric sequence if there is a common difference and if not, write none.
1. 400, 200, 100, 50, . . . Answer: ______________Common Ratio: __________
2. 15, 30, 45, 60, . . . Answer: ______________Common Ratio: __________
3. 1, 2, 4, 8, . . . Answer: ______________Common Ratio: __________
#1. r = 1/2
#2. arithmetic sequence, d=15
#3. r = 2
You can find the common ration just by dividing any term by the one before it.
If you do that with two different terms and the quotients are the same, then you're home free. (Assuming they haven't slipped in any ringers)
1. Differences:
400-200 = 200.
200-100 = 100.
100-50 = 50.
No common difference.
Common ratios: 400/200 = 200/100 = 100/50 = 2/1.
2. Common differences: 30-15 = 45-30 = 60-45 = 15.
Common ratios: 30/15 = 60/30 = 2/1.
3. Common difference: None.
Common ratios: = 2/1 = 8/4.
Sure, I can help you with that! To determine if a sequence is a geometric sequence, we need to check if there is a common ratio between consecutive terms.
Let's go through each question one by one:
1. 400, 200, 100, 50, . . .
To find if there is a common ratio, we need to divide any term by the previous term. Let's take the second term 200 and divide it by the first term 400:
200 / 400 = 1/2
Now, let's take the third term 100 and divide it by the second term 200:
100 / 200 = 1/2
We can see that each term is half of the previous term, so the common ratio is 1/2.
Therefore, the answer for this question is a geometric sequence with a common ratio of 1/2.
2. 15, 30, 45, 60, . . .
Again, let's divide any term by the previous term to check for a common ratio. Taking the second term 30 and dividing it by the first term 15:
30 / 15 = 2
Now, let's take the third term 45 and divide it by the second term 30:
45 / 30 = 3/2
As we can see, there is no consistent common ratio between consecutive terms in this sequence. Therefore, the answer for this question is none (no common ratio).
3. 1, 2, 4, 8, . . .
Once more, let's divide any term by the previous term to determine the common ratio. Dividing the second term 2 by the first term 1:
2 / 1 = 2
Now, dividing the third term 4 by the second term 2:
4 / 2 = 2
We can observe that each term is doubled compared to the previous term. Thus, the common ratio in this sequence is 2.
Therefore, the answer for this question is a geometric sequence with a common ratio of 2.
I hope this explanation helps you understand how to determine if a sequence is a geometric sequence and find the common ratio. If you have any further questions, feel free to ask!