Identify the sequence as arithmetic, geometric, or neither. Explain your answer.
1.6, 0.8, 0.4, 0.2, . . .
I think it is geometric - divisible by 1/2...? Is that right?
Amanda's answer is not correct. 1.6 multiplied by two is not 0.8, it is 3.2 so that's incorrect. 1.6 divided by two is actually 0.8 so the answer Steve provided is factual.
the problem is the "divisible"
divisible by 1/2 means that something is a multiple of 1/2, such as 1,7/2, etc.
2/7 is not divisible by 1/2
Now, for our sequence, one usually states how each successive term is generated, in this case
divide by 2
or
multiply by 1/2
algebraically,
a = 1.6
r = 1/2
where a is the 1st term and r is the ratio between terms.
can you tell me how it should be stated then Steve?
How should it stated?
ok - I understand - thank you for explaining
Yes, you are correct. To determine whether a sequence is arithmetic, geometric, or neither, we need to examine the differences or ratios between the terms.
In this sequence, the terms are halving from one term to the next. The ratio between consecutive terms is 1/2 or 0.5. This means that each term is obtained by multiplying the previous term by 0.5.
Since the terms are related to each other by a constant ratio (0.5), we can conclude that this sequence is a geometric sequence.
Therefore, the sequence 1.6, 0.8, 0.4, 0.2,... is a geometric sequence with a common ratio of 0.5.