Sigma to Series
8
Sigma 6(-2)n-1
n=1
6+(-12)+24+...+(-768)
2+6+18+...+13,122
9
Sigma 2(3)n-1
n=1
1.A rabbit population grew in the following pattern: 3, 12, 48, 192,.... If all the rabbits live and the pattern continues, how many rabbits will be in the 8th generation?
a8=49,152 rabbits
1.A bacteria culture started out with 1500 bacteria and doubles in number every hour. How many bacteria total are there after 14 hours?
24,574,500 bacteria.
14
Sigma 3(3)n-1
n=1
3+9+27+...+4,782,969
9+18+36+...+1,152
8
Sigma 9(2)n-1
n=1
2.A workman agreed to work under the following conditions: His salary for the first day of work will be $2, for the second day of work $4, and for the third day of work $8, and so on. How long does he have to work to earn 16384?
14 days.
2. The population of cats on an island is currently 1000 and is increasing 4% each year. How many cats will be the population on the 20th year?
2,107 cats.
6
Sigma 1/2(3/4)n-1
n=1
1/2+3/8+9/32+...+243/2048
3+27+243+...+19,683
5
Sigma 3(9)n-1
n=1
3.If you have been hired at an annual salary of $18,000 and expect to receive annual increases of 5%, how much money will you have in total for 5 years?
$99,461.3625
3. If you receive $0.04 on the first day, $0.12 on the second day. $0.36 on the third day, and double the amount on each successive day, what is the total amount of money that you will receive in 30 days?
$10,737,418.23
27
Sigma 4(3)n-1
n=1
4+12+36+...+26,244
81+405+2,025+...+50,625
5
Sigma 81(5)n-1
n=1
4. The value of a new car is $35,000. If the car depreciates by 5% in value each year, what will be the value of the car 16 years later?
$16,215.19306
4. The size of an insect population reduce 3% every week. If there are 30000 insects initially present, how many insects will there be in 5 weeks?
26,559 insect.
21
Sigma -6(5)n-1
n=1
-6+(-30)+(-150)+...+(-5.722045898x1014)
1-4+16-64+...+262,144
10
Sigma 1(-4)n-1
n=1
5.The prizes are awarded according to the following rule : the first prize $1500 ; the second prize is 3/4 of the first prize, the third prizes 3/4 of the second prize, and so on, till the 25th prize for the last arriving athlete.How much money do the organizers need to have for the prize fund?
$5,995.484736
5. Sloan went on a 4 day hiking trip. Each day, she walked 20% more than distance that she walked the day before. She walked a total of 27 kilometers. What is the distance Sloan walked in the 1st day of the trip?
5 kilometers.