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

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.)

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 $$\displaystyle{d}={2}.$$