Find the 100th and the nth term for each of the following sequences. a. 1,3,5,7 b. 50, 90, 130 c. 1.3.9. ... d. 9.93.95.97 e. 142+7.229.142+8.229.142 +9.229

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 + 10c) the 100th term is 60.7 and the nth term is .6n +.7d) The 100th term is 11.91 and the nth term is 9.91 + 0.02ne) 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 sequencesa) 1, 3, 5, 7...First term = 1Difference = 2nth term = [tex]1+2(n-1)[/tex] = 1 + 2n - 2 = 2n - 1100th term= 2(100) - 1 = 200 - 1 = 199b) 50, 90, 130... First term = 50Difference = 40nth term = 50 + 40(n - 1) = 50 +40n - 40 = 40n + 10 100th term = 40(100) + 10 = 4000 + 10 = 4010c) 1.3, 1.9...First term = 1.3Difference = .6 nth term = [tex]1.3 + .6(n-1)\\1.3 +.6n-.6\\.6n+.7[/tex]100th term = .6(100) +.7 = 60 + .7 = 60.7d) 9.93, 9.95, 9.97...First term = 9.93Difference = .02nth term = [tex]9.93 + .02(n-1)\\9.93+.02n-.02\\9.91 +.02n[/tex]100th term = 9.91+.02(100) = 9.91 + 2 = 11.91e) 142+7.229, 142+8.229...First term = 142 +7.229Difference = .02nth 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