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Sigma to Series

100

 8

Sigma 6(-2)^n-1

ⁿ⁼¹

6+(-12)+24+...+(-768)

200

 14

Sigma 3(3)^n-1

n=1

3+9+27+...+4,782,969

300

6

Sigma 1/2(3/4)^n-1

n=1

1/2+3/8+9/32+...+243/2048

400

27

Sigma 4(3)^n-1

n=1

4+12+36+...+26,244

500

21

Sigma -6(5)^n-1

n=1

-6+(-30)+(-150)+...+(-5.722045898x10¹⁴)

Series to Sigma

100

2+6+18+...+13,122

9

Sigma 2(3)^n-1

ⁿ⁼¹

200

9+18+36+...+1,152

8

Sigma 9(2)^n-1

ⁿ⁼¹

300

3+27+243+...+19,683

5

Sigma 3(9)^n-1

ⁿ⁼¹

400

81+405+2,025+...+50,625

5

Sigma 81(5)^n-1

ⁿ⁼¹

500

1-4+16-64+...+262,144

10

Sigma 1(-4)^n-1

n=1

Word Problems 1

100

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 

200

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.

300

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

400

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

500

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

Word Problems 2

100

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.

200

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.

300

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

400

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.

500

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.