Answer
General Term $a_{n}=23-3n$
No. of cans in fifth row $=8$
No. of rows in the display $=7$
No. of cans in the top row $=2$
Work Step by Step
No. of cans in first row $a_{1}=20$
No. of cans in second row $a_{2}=17$
Common difference $d = a_{2}- a_{1} = 17-20 = -3 $
To find general term,
$a_{n}=a_{1}+(n-1)d$
$a_{n}=20+(n-1)(-3)$
$a_{n}=20-3n+3$
$a_{n}=23-3n$
No. of cans in fifth row,
$a_{n}=23-3n$
$a_{5}=23-3 (5)$
$a_{5}=23-15$
$a_{5}=8$
To find No. of rows, let $a_{n}=0$
$a_{n}=23-3n$
$23-3n=0$
$3n=23$
$n= \frac{23}{3}$
$n= 7\frac{2}{3}$
No. of rows can not be in fraction. So, $n=7$
There are $7$ rows in the display.
No. of cans in the top row,
$a_{n}=23-3n$
$a_{7}=23-3 (7)$
$a_{7}=23-21$
$a_{7}=2$
