Help on 5 problems, please...geometric sequences, series?

[dementia0787]

I am absolutely terrible at mathematics, and I have a final soon. A few worksheets were handed out on Monday as study guides, and so far these five problems have me puzzled.First problem:Find the sum of the first 5 terms of the geometric sequence.The second term is 3 and the third term is 3/7.Second problem:Find the sum of each infinite geometric series, if possible.16 + 8 + 4 + . . .Third problem:Find the sum of each infinite geometric series, if possible.81 - 27 + 9 - . . .Fourth problem:Write decimal in fraction form. Check the answer by performing a long division.0.18 with a bar over the 18 (infinity)Fifth problem:John has $20000 in a safe deposit box. Each year, he spends 12% of what is left in the box. How much will be in the box after 16 years? Please round the answer to the nearest cent.Any help would be much appreciated. Thanks!No more answers needed. Will be selecting the answer below as best answer. Thanks!

[Letao12]

1) The two terms given to you tell you that the common ratio is 1/7. Then you can get:First term = 21Second term = 21 * (1/7) = 3Third term = 3 * (1/7) = 3/7Fourth term = (3/7) * (1/7) = 3/49Fifth term = (3/49) * (1/7) = 3/343Add the five together, you get 8403/343 = 24.498542) The first term is 16, and the common ratio is 1/2 because 16 * 1/2 = 8, 8 * 1/2 = 4, etc. The formula for the sum is(first term) / (1 - ratio)So plug the numbers into the formula to get(16) / (1 - 1/2) = 32 is the sum3) Same idea, the common ratio is now -1/3 because 81 * (-1/3) = -27, -27 * (-1/3) = 9, etc. Use the formula again(81) / (1 - -1/3) = 60.754) Write the infinite decimal as a geometric series:0.18 bar = 0.18 + 0.0018 + 0.000018 + 0.00000018 + ...The first term is 0.18, and the common ratio is 1/100. Use the formula to find the sum:0.18 / (1 - 1/100) = 18/99 = 2/11Try dividing 2 by 11 with long division, and you'll get 0.181818... back.5) After each year, 88% of what was in the box remains. So after the first year he has20000 * 0.88 leftAfter two years he has20000 * 0.88 * 0.88 leftAfter three years he has20000 * 0.88^3 (to the third power) left...So after 16 years, he will have20000 * 0.88^16 = 2586.74 left.