Exercise 87 Page 225

To find the value of any term, given a recursive equation, we need to substitute the value of the previous term. For example, if we wanted to find the second term, we would use $t(1).$ Repeating this process, we can find the rest of the terms.

Term $n+1$	$t(n+1)=t(n)-5$	Term value
$2$	$t(2)=t(1)-5$	$3$
$3$	$t(3)=t(2)-5$	$\text{-}2$
$4$	$t(4)=t(3)-5$	$\text{-}7$
$5$	$t(5)=t(4)-5$	$\text{-}12$

To find the value of any term, given a recursive equation, we need to substitute the value of the previous term. For example, if we wanted to find the second term, we would use $t(1).$ Repeating this process, we can find the rest of the terms.

Term $n+1$	$t(n+1)=(t(n){)}^{\text{-}1}$	Term value
$2$	$t(2)=(t(1){)}^{\text{-}1}$	$\frac{1}{2}$
$3$	$t(3)=(t(2){)}^{\text{-}1}$	$2$
$4$	$t(4)=(t(3){)}^{\text{-}1}$	$\frac{1}{2}$
$5$	$t(5)=(t(4){)}^{\text{-}1}$	$2$