Question

Please help Asap!

Directions: Write a recursive rule and an explicit rule for each arithmetic sequence.

86, 101, 116, 131, 146,...

112, 110, 108, 106, 104,...

Answer 1

Explanation:

86,101,116,131,146,...

a=86

c.d d=101-86=15

explicit formula

`a_(n)=a+(n-1)d\\a_(n)=86+(n-1)15=86+15n-15=71+15n,n \in I,n>0\\`

recursive formula

`a_(n)=a_(n-1)+15,a_(1)=86,n \in I,n \geq 2`

2.

112,110,108,106,104,...

a=112

c.d d=110-112=-2

explicit formula

`a_(n)=112+(n-1)(-2) =112-2n+2=114-2n,n \in I,n>0`

recursive formula

`a_(n)=a_(n-1)-2,a_(1)=112,n \in I,n \geq 2`