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 \(d=2\).
0

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