I need alot of help with geometric sequences and series
I've answered loads of the questions but I get stuck on the part c and d of them all. so can some one help me asap?
here are the questions.
1) The second term in a geometric series is 80 and the fifth term is 5.12.
sum to infinity= 333 (1/3)
d)Calculate the difference between the sum to infinity of the series and the sum of the first 14 terms of the series, giving your answer in the form a*10^n, where 1(</=)a<10 and n is an integer.
2)The nth term of a sequence is Un, where Un=95(4/5)^n, n= 1 2 3 ...
c) to 3 significant figures calculate
d) to 3 significant figures calculate the sum to infinity of the series whose 1st term is U1, and whose nth term is Un. ( the dot is next to the 'n')
3)The 3rd and 4th terms of a G.S are 6.4 and 5.12.
sum to infinity=50
d)Calculate the difference between the sum to infinity and the sum of the first 25 terms of the series.
4)A saving scheme pays 5% per annum compound interest. A deposit of £100 is invested in this scheme at the start of each year. at the start of 3 years= £315.25
b)Find the amount in the scheme at the start of the fortieth year, after the annual deposit has been made.
5)A liquid is kept in a barrel. At the start of the year the barrel is filled with 160 litres of the liquid.Due to evaporation, at the end of every year the amount in the barrel is reduced by 15% of its volume at the start of the year.
At the start of each year a new barrel is filled with 160 litres of liquid so that, at the end of 20 years, there are 20 barrels containing liquid.
c) Calculate the total amount of liquid, to the nearest litre, in the barrels at the end of 20 years.
I know that that is quite a lot of questions but I'm really stuck on them all, I've tried loads of methods but nothing seams to help. All help will be appreciated greatly!
Thanks in advance.