Question

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

Answer 1

4.

$a_1=-20,\ a_3=-15\\\\2d=a_3-a_1\to 2d=-15-(-20)\to2d=-15+20\to2d=5\to d=2.5\\\\a_n=a_1+(n-1)d\to a_n=-20+(n-1)(2.5)=-20+2.5n-2.5=2.5n-22.5\\\\a_2=2.5(2)-22.5=5-22.5=-17.5\\\\a_4=2.5(4)-22.5=10-22.5=-12.5\\\\a_6=2.5(6)-22.5=15-22.5=-7.5$

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

f(n)|  -20  | -17.5 |  -15  |-12.5|  -10  | -7.5 |

First term: -20     Common Difference: 2.5

Explicit Rule:  $a_n=2.5n-22.5$       Recursive Rule: $a_1=-20,\ a_n=a_{n-1}+2.5$

5.

$a_1=123,\ a_2=131\\\\d=a_2-a_1\to d=131-123=8\\\\a_n=a_1+(n-1)d\to a_n=123+(n-1)(8)=123+8n-8=8n+115\\\\a_3=8(3)+115=24+115=139\\\\a_5=8(5)+115=40+115=155\\\\a_6=8(6)+115=48+115=163$

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

f(n)|  123  |  131   | 139 | 147  |  155  | 163 |

First term: 123      Common Difference: 8

Explicit Rule:  $a_n=8n+115$       Recursive Rule: $a_1=20,\ a_n=a_{n-1}+8$