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diomedes.

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## Homework Statement

__Background__: Jack's wife Jill, mindful of the water restrictions is determined to carry buckets of bath water out of the house to water bean stalks.

She carries out 18 litres of water on the first day.

The amount of water Jill carries out A

_{n}, in litres on the

*n*th day is given by the difference equation: A

_{n+1}=0.96*A

_{n}+2 , A

_{1}=18

__: Determine the total amount of water Jill recycles in the first week.__

**Specific**## Homework Equations

A

_{n+1}=0.96*A

_{n}+2 , A

_{1}=18

## The Attempt at a Solution

Ok, well I've been working out the answer by finding the total amount recycled each day by manually putting the values into the formula: 1-18 ; 2-19.28 ; 3-20.51 ; 4-21.69 etc and then adding for the total (151.16), but this doesn't seem an efficient way of finding the answer. Is there a formula for the sum (similar to the sums of airthmetic/geometic sequences)?

It is quite possible the answer to this is impossible/obvious, so don't be too harsh :P :)