Sequence and Series

Sequence

Series

Arithmetic

Geometric

Infinite

100

Determine the first term of the arithmetic sequence in which the 16th term is 110 and the common difference is 7.

What is 5

100

Find S₁₀for the following series,

10+7+4+...

What is S₁₀=-35

100

True or False

Is the term 89 part of the following sequence.

t_n=107-3n

What is true

100

Suppose the colour of jeans fades by 5% each time they are washed. How many washings would it take so that only 25% of the original colour remains in the jeans?

What is 27 washes

100

Determine whether the following infinite geometric series is convergent or divergent

0.1+0.05+0.025+0.0125+...

What is convergent

200

The first term of an arithmetic sequence is 5y and the common difference is -3y. What is t₁₅of the sequence?

-what is t₁₅=-37y

200

It's About Time in Langley, British Columbia is Canada's largest custom clock manufacturer. They have a grandfather clock that, on hours, chimes the number of hours that corresponds to the time of day. How many times does the clock chime in 24 hrs?

what is 156 times

200

Determine the value of n for the given value.

-19,-13,-7,..., 119

What is n=24

200

A persons kidney filters out 18% of a particular medicine every two hours. How much medicine remains after 12 hrs if the initial dosage was 250mL

What is 76.0ml

200

Determine the sum of the infinite geometric series

2+2(0.6)+2(0.6)²+2(0.6)³+...

What is 5

300

Determine the formula for the nth term of the of the geometric sequence.

192,-48,12,-3,...

What is t_n=192(-1/4)^n-1

300

A fan out system is used to communicate with a large group of people. The person in charge pf the contact committee relays the information to four people.Each of those people notifies four more people who turn around and notify four more people. If there is 7 levels to this group how many people are in the group?

What is 4096

300

The sum of the first nine terms of an arithmetic series is 162, and the sum of the first 12 terms is 288. Determine the first five terms.

What is 2+6+10+14+18

300

An advertising company designs a campaign to introduce a new product to a metropolitan area. The company determines 1000 people are aware of the product at the beginning of the campaign. The number of new people awareness increase 40% every 10 days during the campaign. Determine the total number of people who will be aware of the product after 100 days.

What is 98 739

300

If the first term of an infinite geometric series is -18 and the sum is -45 then what is the common ratio?

What is r= 3/5 or 0.6

400

The population of a city increases by 6.5% each year for ten years. If the initial population is 200 000, what is the population after 30 years?

What is 226 845

400

The sum of the first 7 terms of a geometric series is 89. The sum of the first 8 terms is 104, what is the value of the 8th term?

What is 15

400

Find the first five terms of the arithmetic series where t₁₂=35 and S₂₀=610

What is 2+5+8+11+14

400

A doctor prescribes 200mg of medication on the first day of treatment. The dosage is reduced by one half on each successive day for one week. What is the total amount of medication prescribed?

What is 397mg

400

The sum of an infinite series is 120 and the common ratio is -2/5 or -0.4. Then What is t₁?

What is t₁= 168

500

If x+2, 2x+1, and 4x-3 are three consecutive terms in a geometric sequence, determine the value of the common ratio and the first three terms?

What is r=5/3 and 9,15,25

500

What is the sum of geometric series?

4-16+64-...-65 536

What is S₁₀= (29 524)/ 27

500

Determine S₃₀for the following series.

5+5.3+5.6+...

What is S₃₀=280.5

500

If every person has two parents, four grandparents, eight great-grandparents, and so on. Determine the number of ancestors a person has back through ten generations.

What is S₁₀=2046

500

The length of an initial swing of a pendulum is 90cm. Each successive swing is 0.7 times the length of the previous swing. If the process continues forever, how far will the pendulum swing?

What is 300 cm