Question

1. write the recursive arithmetic rule:

a. 12, 19, 26, 33...
( t(n + 1) = )
( t(1) = )
b. 9, -2, -13, -24...
( t(n + 1) = )
( t(1) = )

Explanation:

Step1: Find common difference (a)

$19-12=7$, $26-19=7$, $33-26=7$

Step2: Define recursive rule (a)

$t(n+1)=t(n)+7$

Step3: Set first term (a)

$t(1)=12$

Step4: Find common difference (b)

$-2-9=-11$, $-13-(-2)=-11$, $-24-(-13)=-11$

Step5: Define recursive rule (b)

$t(n+1)=t(n)-11$

Step6: Set first term (b)

$t(1)=9$

Answer:

a. $t(n+1)=t(n)+7$, $t(1)=12$
b. $t(n+1)=t(n)-11$, $t(1)=9$