Answer:
a) the 100th term is 199 and the nth term is 2n-1.
b) the 100th term is 4010 and the nth term is 40n + 10
c) the 100th term is 60.7 and the nth term is .6n +.7
d) The 100th term is 11.91 and the nth term is 9.91 + 0.02n
e) The 100th term is 142 +106.229 and the nth term is 142 + (6.229+n)
Step-by-step explanation:
The formula to find the nth term of a sequence is:
[tex]a_{n}=a_{1}+d(n-1)[/tex]
Where [tex]a_{n}[/tex]is the nth term, [tex]a_{1}[/tex]is the first one and d is the difference between each term.
So now we're going to apply this to our sequences
a) 1, 3, 5, 7...
First term = 1
Difference = 2
nth term = [tex]1+2(n-1)[/tex] = 1 + 2n - 2 = 2n - 1
100th term= 2(100) - 1 = 200 - 1 = 199
b) 50, 90, 130...
First term = 50
Difference = 40
nth term = 50 + 40(n - 1) = 50 +40n - 40 = 40n + 10
100th term = 40(100) + 10 = 4000 + 10 = 4010
c) 1.3, 1.9...
First term = 1.3
Difference = .6
nth term = [tex]1.3 + .6(n-1)\\1.3 +.6n-.6\\.6n+.7[/tex]
100th term = .6(100) +.7 = 60 + .7 = 60.7
d) 9.93, 9.95, 9.97...
First term = 9.93
Difference = .02
nth term = [tex]9.93 + .02(n-1)\\9.93+.02n-.02\\9.91 +.02n[/tex]
100th term = 9.91+.02(100) = 9.91 + 2 = 11.91
e) 142+7.229, 142+8.229...
First term = 142 +7.229
Difference = .02
nth term = [tex](142 + 7.229) +1(n-1)\\(142+7.229)+n-1\\142 + (7.229+n-1)\\142 + (6.229+n)[/tex]
100th term= 142 + (6.229 + 100) = 142 + 106.229
