Question

15 POINTS HELP PLEASE! Complete the table and pattern. Determine the common difference. Write the explicit rule.

Answer 1

9.

`a_1=-252,\ a_2=-243\\\\d=a_2-a_1\to d=-243-(-252)=-243+252=9\\\\a_n=a_1+(n-1)d\to a_n=-252+(n-1)(9)=-252+9n-9=9n-261\\\\a_3=9(3)-261=27-261=-234\\\\a_5=9(5)-261=45-261=-216\\\\a_6=9(6)-261=54-261=-207`

n | 1 | 2 | 3 | 4 | 5 | 6 |

f(n)| -252 |-243 | -234|-225| -216 | -207 |

First term: -252 Common Difference: 9

Explicit Rule:
`a_n=9n-261` Recursive Rule:
`a_1=-252,\ a_n=a_(n-1)+9`

10.

`a_1=72,\ a_3=54,\ a_4=45\\\\d=a_4-a_3\to d=45-54=-9\\\\a_n=a_1+(n-1)d\to a_n=72+(n-1)(-9)=72-9n+9=81-9n\\\\a_2=81-9(2)=81-18=63\\\\a_5=81-9(5)=81-45=36\\\\a_6=81-9(6)=81-54=27`

n | 1 | 2 | 3 | 4 | 5 | 6 |

f(n)| 72 | 63 | 54 | 45 | 36 | 27 |

First term: 72 Common Difference: -9

Explicit Rule:
`a_n=81-9n` Recursive Rule:
`a_1=-252,\ a_n=a_(n-1)-9`