Answer:
a). 325 boxes per day
b). 717000 boxes
Step-by-step explanation:
A candy shop produced 100 boxes of candies per working day in January.
From the next month shop produced 25 more boxes of candies per working day from the next month.
So the sequence formed for each month will be,
100, 125, 150, 175........
This sequence has a common difference 'd' = 125 - 100 = 25, in every subsequent month.
Therefore, it's an arithmetic progression.
First term of the sequence is 'a' = 100.
Explicit formula for the nth term of this sequence is
[tex]T_{n}=a+(n-1)d[/tex]
where a = first term
and d = common difference
n = number of term
a). For October means n = 10, productivity will be
[tex]T_{10}=100+(10-1)(25)[/tex]
= 100 + 225
= 325 boxes per day
b). If working days in a month are 20 then number of boxes produced in every month will be
2000, 12500, 15000........
So the sequence has first term 'a' = 2000
Common difference 'd' = 12500 - 2000 = 10500
Sum of the sequence for 12 terms, 'n' = 12
Total boxes produced = [tex]\frac{n}{2}[2a+(n-1)d][/tex]
= [tex]\frac{12}{2}[(2\times 2000)+(12-1)10500][/tex]
= 6[4000 + 115500]
= 717000 boxes
