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# 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.) # 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 asked 2020-11-09
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.)

## Answers (1) 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 $$d=2$$.

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Previous studies show that $$\sigma_1 = 19$$.
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