A small company producing children’s toys plans an increase in output.

The number of toys produced is to be increased by 8 each week until the

weekly number produced reaches 1000. In week 1, the number to be

produced is 280; in week 2, the number is 288; etc. Show that the weekly

number produced will be 1000 in week 91.

****From week 91 onwards, the number produced each week is to remain at 1000. Find the total number of toys to be produced over the first 104 weeks of the plan.****

**just the one in bold, thanks **

Guest Aug 11, 2022

#1**0 **

Case 1: Weeks 91 - 104

There are \(104 - 91 + 1 = 14\) weeks, so they produce a total of \(14 \times 1000 = 14000 \) toys.

Case 2: Weeks 1 - 91

We have an arithmetic sequence with a starting term of 280, a final term of 100, and 91 terms.

This means that the sum is\((1000 + 280) \div 2 \times 91 = 58240\)

So, they produced a total of \(58240 + 1400 = \color{brown}\boxed{59640}\)

BuilderBoi Aug 11, 2022