A water butt standing beside a farm barn collects rainwater running off the roof. The amount collected increases by 12 litres every week. In week 7 the wate...
Question 1 Report
A water butt standing beside a farm barn collects rainwater running off the roof. The amount collected increases by 12 litres every week. In week 7 the water butt holds 134 litres.
- Find the amount of water in the water butt in week 1. (2)
- Write down the amount of water in the water butt in week 8. (1)
Answer Details
When a term partway through an arithmetic sequence is known, earlier terms can be found by working backwards, subtracting the common difference the right number of times; later terms are found by adding it forwards.
The water butt gains 12 litres each week, and week 7 holds 134 litres. Working back 6 steps of 12 to reach week 1 gives \[134 - 6(12) = 134 - 72 = 62 \text{ litres}\] [2 marks]
Adding one more step of 12 to the week 7 total gives week 8: \[134 + 12 = 146 \text{ litres}\] [1 mark]
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