Arithmetic Grade 11 Math Help!

[Eccentric]

I need to find the indicated sum for each geometric series but i can't figure it out.
1) S7 for 972 + 324 ?108.....
2?S6 for 1 - 1/2 + 1/4 - ...
3) 729 +243 + 81 + ... +1
4) 1200 ?120??12?+ ... 0.0012

5) The first prize in a lottery is $100 000. Each succeeding winning number pays %40 as much as the winning number before it. How much is paid in prizes if 6 numbers are drawn?

6) The air in a hot-air balloon cools as the balloon rises. If the air is not reheated, the balloon rises more slowly every minute. Suppose that a hot-air balloon rises 50 min in the first minute. In each succeeding minute, the balloon rises %70 as far as it did in the previous minute. How far does the balloon rise in 7 min, to the nearest metre?

Your help is very much appreciated.
Atleast help on one question is very greatful. I'm VERY SORRY for my indulence.

 

[agodina]

Question 5:

For the first number (100.00) multiply it by .4.

You will get forty dollars (40.00)

Next multiply that number (40.00) by .4.

You will get sixteen (16.00) dollars.

Do this four more times (16.00*.4, etc).

 

[agodina]

Question 6:

Same concept (I think you meant to say 'balloon rises 50m').

Multiply 50 by .7

You will get 35 (2nd minute).

Next multiply 35 by .7

You will get 24.5 (3rd minute; rounded up that's 25m)

Keep doing this (24.5*.7, etc.) until you reach seven minutes.