6.
[tex]a_1=529,\ a_2=508\\\\d=a_2-a_1\to d=508-529=-21\\\\a_n=a_1+(n-1)d\to a_n=529+(n-1)(-21)=529-21n+21=550-21n\\\\a_4=550-21(4)=550-84=466\\\\a_5=550-21(5)=445\\\\a_6=550-21(6)=424[/tex]
n | 1 | 2 | 3 | 4 | 5 | 6 |
f(n)| 529 | 508 | 487 | 466 | 445 | 424 |
First term: 529 Common Difference: -21
Explicit Rule: [tex]a_n=550-21n[/tex] Recursive Rule: [tex]a_1=529,\ a_n=a_{n-1}-21[/tex]
7.
[tex]a_1=7.5,\ a_2=9\\\\d=a_2-a_1\to d=9-7.5=1.5\\\\a_n=a_1+(n-1)d\to a_n=7.5+(n-1)(1.5)=7.5+1.5n-1.5=1.5n+6\\\\a_4=1.5(4)+6=6+6=12\\\\a_6=1.5(6)+6=9+6=15[/tex]
n | 1 | 2 | 3 | 4 | 5 | 6 |
f(n)| 7.5 | 9 |10.5 | 12 | 13.5 | 15 |
First term: 7.5 Common Difference: 1.5
Explicit Rule: [tex]a_n=1.5n+6[/tex] Recursive Rule: [tex]a_1=7.5,\ a_n=a_{n-1}+1.5[/tex]
8.
[tex]a_2=120,\ a_3=145\\\\d=a_3-a_2\to d=145-120=25\\\\\a_1=a_2-d\to a_1=120-25=95\\\\a_n=a_1+(n-1)d\to a_n=95+(n-1)(25)=95+25n-25=25n+70\\\\a_5=25(5)+70=125+70=195\\\\a_6=25(6)+70=150+70=220[/tex]
n | 1 | 2 | 3 | 4 | 5 | 6 |
f(n)| 95 | 120 | 145 | 170 | 195 | 220 |
First term: 95 Common Difference: 25
Explicit Rule: [tex]a_n=25n+70[/tex] Recursive Rule: [tex]a_1=95,\ a_n=a_{n-1}+25[/tex]
