The second term, , of a geometric sequence is 44 and the third term, , is 55.
Find the common ratio, , of the sequence.
Find the first term of the sequence, .
Find , the sum of the first 5 terms of the sequence.
Did this page help you?
The second term, , of a geometric sequence is 44 and the third term, , is 55.
Find the common ratio, , of the sequence.
Find the first term of the sequence, .
Find , the sum of the first 5 terms of the sequence.
Did this page help you?
The sum of the first 16 terms of an arithmetic sequence is 920.
Find the common difference, , of the sequence if the first term is 27.5.
Find the first term of the sequence if the common difference, , is 11.
Did this page help you?
The sum of the first 5 terms of a geometric sequence is 461.12.
Find the common ratio, , of the sequence if the first term is 200, given that .
Find the first term of the sequence if the common ratio, is -2.
Give your answer correct to 2 decimal places.
Did this page help you?
The table below shows information about the terms of four different sequences and
|
||||
|
12 | 30 |
|
|
|
12 | 30 |
|
|
80 |
|
|
10 | |
80 |
|
|
10 |
Calculate and the common difference, given that is an arithmetic sequence.
Calculate and the common ratio, given that is a geometric sequence.
Calculate and the common difference, given that is an arithmetic sequence.
Calculate and the common ratio, given that is a geometric sequence.
Did this page help you?
Students are arranged for a graduation photograph in rows which follows an arithmetic sequence. There are 20 students in the fourth row and 44 in the 10th row.
Given there are 20 rows of students in the photograph, calculate how many students there are altogether
Did this page help you?
Marie is an athlete returning to running after an injury and wants to manage the number of kilometres she runs per week. She decides to run 4 km the first week and increase this by 1.5 km each week.
Find the distance Marie ran in the 10th week.
Find the week in which Marie runs 26.5 km.
Marie’s coach says she can start preparing for her next race once she has run a total of 220 km.
Find the week in which Marie will complete this.
Did this page help you?
The eighth term, , of an arithmetic sequence is 18 and the common difference, is 2.
The first and 17th terms of the arithmetic sequence are the third and fifth terms respectively of a geometric sequence.
Did this page help you?
In a geometric sequence, = 160 and the common ratio, is
Find the value of the infinite sum of the sequence.
The first and third terms of the geometric sequence are the seventh and ninth terms respectively of an arithmetic sequence.
Did this page help you?
A sequence can be defined by for .
Write an expression for using sigma notation and find the value of the sum.
Write an expression for using sigma notation and find the value of the sum.
Did this page help you?
A sequence can be defined by , for .
Write an expression for using sigma notation and find the value of the sum.
Write an expression for using sigma notation and find the value of the sum.
Did this page help you?
The kiwi is a flightless bird and is a national treasure in New Zealand. At the start of 2021 there were approximately 68 000 kiwi left, with the population decreasing by 2% every year.
Find the expected population size of kiwis in 2030 assuming the rate of decrease in kiwi population remains the same.
Find the year in which the population of kiwis falls below 50 000 assuming the rate of decrease in kiwi population remains the same.
Did this page help you?
Aaron is working on his cycling in preparation for a triathlon event in 10 months. He cycles a total of 240 km in the first month and plans to increase this by 12.5% each month.
Find the distance Aaron cycles in the fifth month of preparation.
Calculate the total distance Aaron cycles until the triathlon.
Did this page help you?
A geometric sequence has = 0.5 and = 3.
Find
An arithmetic sequence has the same and as the geometric sequence above.
Find and for the arithmetic sequence.
Did this page help you?
The sum of the first two terms of a geometric sequence is and the sum of the infinite geometric sequence is . Find the positive value of the common ratio,
Did this page help you?
The sum of the first eight terms of a sequence is 200.
Given that = 5.75, find:
Find , the sum of the first 12 terms for the arithmetic and geometric sequences found in part (a).
Did this page help you?
The third term of a geometric sequence is 270 and the sixth term is 911.25.
Find the 10th term of the sequence.
Find the sum of the first 21 terms of the sequence.
Give your answer in the form , where and .
Did this page help you?
The table below shows information about the terms of three different sequences, , and .
|
||||||
0.1 |
|
|
2.7 |
|
24.3 | |
24.6 |
|
-19 |
|
62.6 |
|
|
880 |
|
220 |
|
|
27.5 |
Determine whether is an arithmetic or geometric sequence and fill in the table accordingly.
Determine whether is an arithmetic or geometric sequence and fill in the table accordingly.
Determine whether is an arithmetic or geometric sequence and fill in the table accordingly.
Did this page help you?
The 18th term of an arithmetic sequence is 54 and the common difference, is 2.2.
Find the sum of the first 18 terms of the arithmetic sequence.
The first and 18th terms of the arithmetic sequence are the first and second terms respectively of a geometric sequence.
Find the smallest value of such that for the geometric sequence.
Did this page help you?
The fifth term of a geometric sequence is 1 and the common ratio, , is .
Find , the sum of the first five terms of the geometric sequence.
Find the exact value of the infinite sequence.
The first and fifth terms of the geometric sequence are the 20th and 10th terms respectively of an arithmetic sequence.
Find the largest value of such that for the arithmetic sequence.
Did this page help you?
Ashley and Emma are attempting to swim a total of 2000 m each by completing laps of a 25 m pool. Ashley swims her first lap in 17 s and takes 0.2 s longer each lap after that. Emma swims her first lap in 16.5 s and takes 1.01 s times longer each lap after that.
Did this page help you?
The table below shows information about the terms of two different sequences, and
|
||||||
1 |
|
|
|
|||
|
|
|
State which sequence is arithmetic, and which is geometric.
Fill in the missing values in the table.
Find the largest value of such that .
Did this page help you?
A basketball is dropped from a height of 1 m and bounces on the ground times. The height that the basketball reaches after each bounce forms a geometric sequence. The height of the basketball after the first bounce is 80 cm and the height after the third bounce is 51.2 cm.
Find the common ratio, , of the geometric sequence.
Find the height that the ball reaches after the second bounce.
Find the total vertical distance, in metres, travelled by the basketball after the first four bounces.
Find the total distance travelled by the ball.
Did this page help you?
Since the start of 2020, Malcolm has been on a diet and fitness plan aiming to decrease his waist size. To measure his progress, he has been noting when he goes down a size in trousers. In January he wore a size 46, in April he wore a size 44, in July he wore a size 42 and now, in October, he wears a size 40.
Show that the decrease in Malcolm’s size in trousers forms an arithmetic sequence and find how much his size in trousers decreases each month.
Find the month and year when Malcolm’s size in trousers will be 34.
State a more accurate way Malcolm could measure the reduction in his waist size.
Did this page help you?
Grace is a photographer and joins Instagram to advertise her photos. She made one post in the first week and four posts in the fifth week.
Find the week in which Grace will make her 1000th post.
After 11 weeks Grace has 100 followers and after 21 weeks she has 200 followers.
Assuming the increase in Grace’s followers forms a geometric sequence, calculate:
Grace believes that once she reaches 10 000 followers, companies will start paying her to take photographs of their products.
Find the week in which Grace will reach 10 000 followers.
Did this page help you?
The sixth term of an arithmetic sequence is equal to 3 and the sum of the first 12 terms is 12.
Find the common difference and the first term.
Did this page help you?
A geometric sequence has .
Find the common ratio, .
Find .
Find . Give your answer as a fraction.
Find .
Did this page help you?
Julie is starting a new web-based subscription business. She sells her subscriptions for $19.50 per month with customers paying at the start of every month. She has 12 customers ready to sign up in the first month. By the fifth month she has 29 customers.
Given that the increase in customers follows an arithmetic sequence, calculate the number of customers Julie will have in the 9th month
Calculate the revenue Julie’s business will generate by the 17th month. Give your answer correct to the nearest dollar.
Did this page help you?
A football team, SME United, have a new stadium with a maximum capacity of 5000 seats, 1500 seats are reserved for the opposition supporters. SME United have 2195 loyal fans who come to all home matches. The manager has predicted that SME United will gain 45 new loyal fans every match who will come to every home match thereafter.
Based on the manager’s prediction, work out how many matches will be played before the number of unreserved seats run out.
A ticket to one of the matches costs $12.
If the manager's prediction for the increase in loyal fans is correct, and if on average half of the tickets reserved for opposition supporters are sold per game, calculate the revenue that SME United will generate from ticket sales in a 30 match season.
Did this page help you?
Ben and Sam are both cyclists competing in a 22.5 km race at the Herne Hill Velodrome in London, England. One lap of the velodrome is 450 m.
Ben takes a total of 42 minutes to complete the race.
Calculate Ben’s mean lap time in seconds.
Given that each of Ben’s laps took him 1% longer to complete than the previous one, calculate how long it took him (in seconds) to complete his first and last laps.
Sam completes the first lap in 45 seconds and takes 0.2 seconds longer per lap.
Determine who completed the race the first out of Ben and Sam. Justify your answer.
Did this page help you?
The first three terms of a geometric sequence are , and respectively, where .
Find , the fifth term of the sequence. Give your answer as a fraction.
Find the sum of the first seven terms of the sequence.
Did this page help you?
Lucy is considering two investment strategies.
Strategy A requires an initial deposit of $100. At the start of the second month a deposit of $115 would need to be made, with monthly deposits at the start of each month thereafter that are each $15 more than the deposit in the previous month.
Strategy B requires an initial deposit of $90. At the start of the second month a deposit of $93.60 would need to be made, with monthly deposits at the start of each month thereafter that are each 4% more than the deposit in the previous month.
Write an expression, using sigma notation, to represent the total amount invested after months in
Find which monthly deposit from Strategy A would be the last one that is greater than the corresponding monthly deposit from Strategy B.
Find after which monthly deposit the total amount invested in Strategy B would exceed the total amount invested in Strategy A.
Did this page help you?
Calculate the total amount of revenue the restaurant made in the first week. Give your answer correct to 2 decimal places.
During the first week Joshua ran a successful marketing campaign and noticed that during the fourth week the restaurant had an average of 33 guests per evening.
Assuming the growth in average guests per evening follows an arithmetic sequence, find the week during which the restaurant will experience capacity issues.
Calculate the total revenue that the restaurant will generate in its first 10 weeks of being open. Give your answer correct to the nearest dollar.
Did this page help you?
The first term of both an arithmetic and a geometric sequence is 1 and both sequences have the same second term. The 20th term of the arithmetic sequence is five times the third term of the geometric sequence.
Find the possible values of the second term.
Find the possible values of the 10th term for each sequence.
Did this page help you?
The first four terms of an arithmetic sequence are and respectively.
Find the values of and .
Let denote the sum of the first terms of the sequence.
Find the largest value of such that .
Did this page help you?
Guy starts a new job where his base salary is $ per year and his salary will increase by $ every year for years.
Given that at the end of years Guy will have earned $367 200 and his salary after years will be $37 200, show that
Additionally, given that after years Guy’s salary will be $26 400, show that
Find the values of and .
Did this page help you?
In an arithmetic sequence
Show that .
Let and . Find the value of
Did this page help you?
The first three terms of a geometric sequence are , 3 and , where
Show that satisfies the equation
Given that the sequence has an infinite sum, find the value of
Find the sum of the sequence.
Did this page help you?