Question

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)

Polynomial arithmetic
ANSWERED
asked 2021-02-09

Consider the following sequence. \(\displaystyle{s}_{{n}}={2}{n}−{1}\)

a) Find the first three terms of the sequence whose nth term is given.

\(\displaystyle{s}_{{1}}=\)

\({s}_{{2}}=\)

\({s}_{{3}}=\)

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.)

Answers (1)

2021-02-10

The given sequence is, \(\displaystyle{s}_{{n}}={2}{n}-{1}\)

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, \(s_1 = 1\)
\(s_2 = 3\)
\(s_3 = 5\) 

b) The given sequence is \(\displaystyle{s}_{{n}}={2}{n}−{1}.\) The terms of the sequence are 1,3,5,7,... Here,

\(\displaystyle{s}_{{2}}-{s}_{{1}}={3}-{1}\)

\(={2}\)

\({s}_{{3}}-{s}_{{2}}={5}-{3}\)

\(={2}\)

That implies, there exists a common difference between two successive numbers. So, the given sequence is an arithmetic sequence whose common difference is \(\displaystyle{d}={2}.\)

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