+234 1) Find the sum of the arithmetic sequence 7∑ i = 3 (4+i)
Sigma example 1: 7 is above the sigma, i = 3 is below the sigma sign and (4+i) is to the right of the sigma sign.
Answer: 56
2) Find the sum of the geometric series 5∑ i = 1 3(2/3)^i
Answer: 5.2
3) Find the sum of the infinite geometric series if it exists 3/2 - 3/4 + 3/8 + 3/16 ......
4) Solve using binomial theorem (2x-3y)^4
Answer: 16x^4 - 96x^3y + 216x^2y^2 - 216xy^2 +81y^4
5) Find the coefficient of x^3 in the expansion of (2x-4)^7
6) Write recursive rule for sequence 7, 20, 33, 46, 59.....
7) Write recursice rule for sequence 27, 36, 48, 64, 256/2.....
Word Problems
1) Containers are stacked in 20 rows with 2 in the top row, 5 in the 2nd row, 8 in the 3rd row, and so on. How many contianers are in the stack?
2) A certain bacteria culture initially contains 5,000 bacteria and increases by 15% every hour, write a rule for the number of bacteria an present after N hours. Then find how many bacteria are present after 12 hours.
3) A diamond mine yealds 1.8 million carats in its first year. Since then the yearly output decresed by 12%. The owner hopes the mine will produce 50 million carats over its lifetime, if the trend continues can the mine produce this many carats in its lifetime? What is the total amount of carats produced by the mine in its lifetime?
Answer: 15,000,000 Carats
