glasskerfu

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.)

joshyoung05M

Step 1
The given sequence is, ${s}_{n}=2n-1$
a)Find the first three terms of the sequence as shown below.
${s}_{1}=2\left(1\right)-1$
$=2-1$
$=1$
${s}_{2}=2\left(2\right)-1$
$=4-1$
$=3$
${s}_{3}=2\left(3\right)-1$
$=6-1$
$=5$
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 $d=2$.

Jeffrey Jordon