Question

HELP PLEASE 21 POINTS PLEASE HELP ME!!!! <3

Answer 1

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:
`a_(n) = 1134 - 101n` Recursive rule:
`a_(n) = a_(n-1) - 101`

`a_(n) = a_(1) + d(n - 1)`

`a_(n) = 1033 - 101(n - 1)`

`a_(n) = 1033 - 101n + 101`

`a_(n) = 1134 - 101n`

***********************************************************************************

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:
`a_(n) = -49 + 10n` Recursive rule:
`a_(n) = a_(n-1) + 10`

`a_(n) = a_(1) + d(n - 1)`

`a_(n) = -39 + 10(n - 1)`

`a_(n) = -39 + 10n - 10`

`a_(n) = -49 + 10n`

***********************************************************************************

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:
`a_(n) = 5 - 1.25n` Recursive rule:
`a_(n) = a_(n-1) - 1.25`

`a_(n) = a_(1) + d(n - 1)`

`a_(n) = 3.75 - 1.25(n - 1)`

`a_(n) = 3.75 - 1.25n + 1.25`

`a_(n) = 5 - 1.25n`