Wouldn't this sequence be neither geometric and neither arithmetic?
0.0005, 0.005, 0.05, 0.5
I can'f find a pattern.
And also this sequence, it doesnt look arithmetic or geometric
1/5, 1/4, 1/3, 1/2, 1,...
And also this other question:
The first three terms of the sequence defined by tn = -0.3n + 0.5 are
A. 0.5, 0.8, 1.1
B. -0.3, 0.2, 0.7
C. 0.2, -0.1, -0.4
D. -0.3, -0.8, -1.3
How would you do this, I did something with my calculator and got 0.4, so I just chose C as my answer, but how do you actually figure this out?
The first one is GS , the value of r = 10
the 2nd is neither AS nor GS, but the terms can be described by the formula
term(n) = 1/(6-n)
for the last,
let n=1 to get term(1) = -.3(1) + .5 = 0.2
let n=2 to get term(2) = -.3(2) + .5 = -0.1
etc.
what do you think??
Oh okay this makes sense. Thanks so much. So the third term would equal -0.4, when you plug in the three for the term number.
Y8dn
For the first sequence (0.0005, 0.005, 0.05, 0.5), let's analyze if it is geometric or arithmetic.
To check if it is geometric, we need to see if there is a common ratio between each term. To find the common ratio, we can divide each term by the previous one.
0.005 / 0.0005 = 10,
0.05 / 0.005 = 10,
0.5 / 0.05 = 10.
Since we get the same result (10) for each division, we can conclude that the sequence is indeed geometric with a common ratio of 10.
Now let's analyze the second sequence (1/5, 1/4, 1/3, 1/2, 1). Similar to before, we will check if it is geometric or arithmetic.
To check if it is geometric, we need to see if there is a common ratio between each term. Let's divide each term by the previous one:
(1/4) / (1/5) = 5/4,
(1/3) / (1/4) = 4/3,
(1/2) / (1/3) = 3/2,
1 / (1/2) = 2.
The ratios are not consistent, meaning we don't have a constant common ratio. Therefore, we can conclude that this sequence is not geometric. It does not follow any specific pattern, but it is not an arithmetic sequence either.
Now, let's address the third question about the given sequence defined by tn = -0.3n + 0.5. We need to find the first three terms of this sequence.
To do this, we substitute n = 1, 2, and 3 into the given equation:
t1 = -0.3(1) + 0.5 = 0.2,
t2 = -0.3(2) + 0.5 = -0.1,
t3 = -0.3(3) + 0.5 = -0.4.
Therefore, the first three terms of the sequence are 0.2, -0.1, and -0.4 respectively. These terms are found by substituting n = 1, 2, and 3 into the given equation. Comparing these terms to the answer choices, we can see that the correct option is C, which matches the sequence 0.2, -0.1, -0.4.