1)
n 1 2 3 4 5 6
f(n) 1033 932 831 730 629 528
First term (a₁): 1033 Common difference (d): -101
Explicit rule: [tex]a_{n} = 1134 - 101n[/tex] Recursive rule: [tex]a_{n} = a_{n-1} - 101[/tex]
[tex]a_{n} = a_{1} + d(n - 1)[/tex]
[tex]a_{n} = 1033 - 101(n - 1)[/tex]
[tex]a_{n} = 1033 - 101n + 101[/tex]
[tex]a_{n} = 1134 - 101n[/tex]
***********************************************************************************
2)
n 1 2 3 4 5 6
f(n) -39 -29 -19 -9 9 19
First term (a₁): -39 Common difference (d): +10
Explicit rule: [tex]a_{n} = -49 + 10n[/tex] Recursive rule: [tex]a_{n} = a_{n-1} + 10[/tex]
[tex]a_{n} = a_{1} + d(n - 1)[/tex]
[tex]a_{n} = -39 + 10(n - 1)[/tex]
[tex]a_{n} = -39 + 10n - 10[/tex]
[tex]a_{n} = -49 + 10n[/tex]
***********************************************************************************
3)
n 1 2 3 4 5 6
f(n) 3.75 2.5 1.25 0 -1.25 -2.5
First term (a₁): 3.75 Common difference (d): -1.25
Explicit rule: [tex]a_{n} = 5 - 1.25n[/tex] Recursive rule: [tex]a_{n} = a_{n-1} - 1.25[/tex]
[tex]a_{n} = a_{1} + d(n - 1)[/tex]
[tex]a_{n} = 3.75 - 1.25(n - 1)[/tex]
[tex]a_{n} = 3.75 - 1.25n + 1.25[/tex]
[tex]a_{n} = 5 - 1.25n[/tex]
