C2 geometric series question

hi, for part c of this question I am confused. So I used the formula and sub the values in but didnt get the right answer because I need to multiply the bracket by 0.85 as well but I don't get why. I thought a is just 160.
Thanks

Oooh this isn't really a nice question. Here's why you need to multiply by 0.85.

The question is saying that every year for 20 years, we bring a new barrel with 160 litres. After the 20 years:

The 1st barrel has had 20 years of evaporating time. The amount in that barrel = 160 x (0.85)²⁰ litres

The 2nd barrel has had 19 years of evaporating time. The amount in that barrel = 160 x (0.85)¹⁹ litresThe 19th barrel has had 2 years of evaporating time. The amount in that barrel = 160 x (0.85)² litres

The 20th (and last) barrel has had 1 year of evaporating time. The amount in that barrel = 160 x (0.85) litres

Therefore, the total amount in ALL barrels is:

S = 160 x (0.85) + 160 x (0.85)² ... + 160 x (0.85)¹⁹ + 160 x (0.85)²⁰
S = 160(0.85) [1 + 0.85 + 0.85² .... + 0.85¹⁸ + 0.85¹⁹ ]

The square brackets part is your geometric series.
a = 1
r = 0.85
n = 20

Therefore:
S₁ = (1 - 0.85²⁰ ) / (1 - 0.85)
S₁ = 6.40826...

So S = 160(0.85) x 6.40826...
S = 871.5 litres.

That's where the "160 x 0.85" part comes in..

Thanks for replying. Thats a lot to take in! I will try to understand it as I read it again and thanks for helping me with the chemistry question as well.