# Consider the following sequence. s_{n} = 2n − 1 (a) Find the first three terms of the sequence whose nth term is given. s_{1} = s_{2} = s_{3} = (b) Classify the sequence as arithmetic, geometric, both, or neither. arithmetic, geometric bothneither If arithmetic, give d, if geometric, give r, if both, give d followed by r. (If both, enter your answers as a comma-separated list. If neither, enter NONE.)

Question
Polynomial arithmetic
Consider the following sequence.
$$s_{n} = 2n − 1$$
(a) Find the first three terms of the sequence whose nth term is given.
$$s_{1} =$$
$$s_{2} =$$
$$s_{3} =$$
(b) Classify the sequence as arithmetic, geometric, both, or neither. arithmetic, geometric bothneither
If arithmetic, give d, if geometric, give r, if both, give d followed by r. (If both, enter your answers as a comma-separated list. If neither, enter NONE.)

2020-11-10
Step 1
The given sequence is, $$s_{n} = 2n − 1$$
a)Find the first three terms of the sequence as shown below.
$$s_{1} = 2(1) - 1$$
$$=2 - 1$$
$$=1$$
$$s_{2} = 2(2) - 1$$
$$=4 - 1$$
$$=3$$
$$s_{3} = 2(3) - 1$$
$$=6 - 1$$
$$=5$$
Therefore,
$$s_{1} = 1$$
$$s_{2} = 3$$
$$s_{3} = 5$$
Step 2
b)The given sequence is,
$$s_{n} = 2n − 1$$
The tems of the sequence are 1,3,5,7,...
Here, $$s_{2} - s_{1} = 3 - 1$$
$$=2$$
$$s_{3} - s_{2} = 5 - 3$$
$$=2$$
That implies, there exists a common difference between two successive numbers.
So, the given sequence is an arithmetic sequence whose common difference is $$d=2$$.

### Relevant Questions

Consider the following sequence. $$\displaystyle{s}_{{n}}={2}{n}−{1}$$ (a) Find the first three terms of the sequence whose nth term is given. $$\displaystyle{s}_{{1}}={N}{S}{K}{s}_{{2}}={N}{S}{K}{s}_{{3}}=$$ (b) Classify the sequence as arithmetic, geometric, both, or neither. arithmeticgeometric bothneither If arithmetic, give d, if geometric, give r, if both, give d followed by r. (If both, enter your answers as a comma-separated list. If neither, enter NONE.)
For Exercise, determine if the nth term of the sequence defines an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic, find the common difference d. If the sequence is geometric, find the common ratio r. $$a_{n} = 5 \pm \sqrt{2n}$$
Give the first six terms of the following sequences. You can assume that the sequences start with an index of 1.
1) An arithmetic sequence in which the first value is 2 and the common difference is 3.
2) A geometric sequence in which the first value is 27 and the common ratio is $$\frac{1}{3}$$
A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 235 m, and the car completes the turn in 33.0 s. (Enter only the answers in the input boxes separately given.)
(a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors $$\displaystyle\hat{{{i}}}$$ and $$\displaystyle\hat{{{j}}}$$.
1. (Enter in box 1) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+{\left({E}{n}{t}{e}{r}\in{b}\otimes{2}\right)}{P}{S}{K}\frac{{m}}{{s}^{{2}}}\hat{{{j}}}$$
(b) Determine the car's average speed.
3. ( Enter in box 3) m/s
(c) Determine its average acceleration during the 33.0-s interval.
4. ( Enter in box 4) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+$$
5. ( Enter in box 5) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{j}}}$$
For each of the following sequences: @ identify if the sequence is arithmetic, geometric or quadratic’. Justify your response. @ assuming the first item of each sequence is a1, give an expression for aj. (In other words, find a formula for the i-th term in the sequence). @ if the sequence is arithmetic or geometric, compute the sum of the first 10 terms in the sequence $$i 2,-12, 72, -432, 2592,...$$
$$ii 9, 18, 31, 48, 69, 94,...$$
$$iii 14, 11.5, 9, 6.5, 4, 1.5,...$$

A random sample of $$n_1 = 14$$ winter days in Denver gave a sample mean pollution index $$x_1 = 43$$.
Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
$$H_0:\mu_1=\mu_2.\mu_1>\mu_2$$
$$H_0:\mu_1<\mu_2.\mu_1=\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1<\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1\neq\mu_2$$
(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference $$\mu_1 - \mu_2$$. Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
$$\mu_1 - \mu_2$$.
lower limit
upper limit
(h) Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.
We will now add support for register-memory ALU operations to the classic five-stage RISC pipeline. To offset this increase in complexity, all memory addressing will be restricted to register indirect (i.e., all addresses are simply a value held in a register; no offset or displacement may be added to the register value). For example, the register-memory instruction add x4, x5, (x1) means add the contents of register x5 to the contents of the memory location with address equal to the value in register x1 and put the sum in register x4. Register-register ALU operations are unchanged. The following items apply to the integer RISC pipeline:
a. List a rearranged order of the five traditional stages of the RISC pipeline that will support register-memory operations implemented exclusively by register indirect addressing.
b. Describe what new forwarding paths are needed for the rearranged pipeline by stating the source, destination, and information transferred on each needed new path.
c. For the reordered stages of the RISC pipeline, what new data hazards are created by this addressing mode? Give an instruction sequence illustrating each new hazard.
d. List all of the ways that the RISC pipeline with register-memory ALU operations can have a different instruction count for a given program than the original RISC pipeline. Give a pair of specific instruction sequences, one for the original pipeline and one for the rearranged pipeline, to illustrate each way.
Hint for (d): Give a pair of instruction sequences where the RISC pipeline has “more” instructions than the reg-mem architecture. Also give a pair of instruction sequences where the RISC pipeline has “fewer” instructions than the reg-mem architecture.
$$\{9=\frac{10}{11}n\}$$
What type of sequence is $$9=\frac{10}{11}n$$
The general term of a sequence is given $$a_{n} = (1/2)^{n}$$. Determine whether the sequence is arithmetic, geometric, or neither.