Answer
676
Work Step by Step
Model the problem using an arithmetic sequence $a_n$. We are given the data :
$a_{1}=123$
$a_{2}=112$
$a_{2}=a_{1}+d$ (determine the common difference d)
$d=a_{2}-a_{1}=112-123=-11$
$d=-11$
$n=8$
$a_{8}=a_{1}+(8-1) d=123+7(-11)=46$
$S_{8}=\frac{8(123+46)}{2}=676$
(In order to estimate the total number of bales made after the farmer takes anther trips (thus a total of $2+6=8$ trips $)$ is the sum of the first 8 terms of the sequence, using the formula:
$S_{n}=\frac{n\left(a_{1}+a_{n}\right)}{2}$
First we determine $a_{8}$ using the formula:
$a_{n}=a_{1}+(n-1) d$)
