Write down the next two terms for each arithmetic sequence:
4, 8, 12, 16
2, 3.5, 5, 6.5
6, 2, - 2, - 6
- 8, - \dfrac{23}{3}, - \dfrac{22}{3}, - 7
State the common difference for each arithmetic sequence:
- 6, - \dfrac{39}{7}, - \dfrac{36}{7}, - \dfrac{33}{7}\ldots
330, 280, 230, 180\ldots
Write the first four terms in each of the following arithmetic sequences:
The first term is - 8 and the common difference is 2.
The first term is 3 and the common difference is - 5.
The first term is a and the common difference is d.
Find the missing terms in the following arithmetic sequences:
5 , ⬚ , -1 , - 4 , ⬚
⬚, - 11, ⬚, - 19, ⬚
Which of the following sets of numbers is an arithmetic sequence:
State the common difference of the arithmetic sequence found in part (a).
The first term of an arithmetic progression is 3 and the common difference is 4.
Find the 15th term of the sequence.
Is 202 a term of the sequence?
Find the first term of the sequence that exceeds 1000.
The nth term in an arithmetic sequence is given by the formula T_{n} = 14 + 5 \left(n - 1\right).
Find a, the first term in the sequence.
Find d, the common difference.
Find the 10th term in the sequence.
The nth term in an arithmetic sequence is given by the formula T_{n} = - 9 n + 19.
Find a, the first term in the sequence.
Find d, the common difference.
Find the 9th term in the sequence.
For each of the following general terms of an arithmetic sequence:
Write down the first four terms.
Find the common difference.
T_{n} = 11 + \left(n - 1\right) \times 10
T_{n} = - 7 - 3 \left(n - 1\right)
T_{n} = 3 n + 8
For each of the following arithmetic sequences:
Find d, the common difference.
State the equation for finding T_{n}, the nth term in the sequence.
Find the 9th term in the sequence.
6, 16, 26 , \ldots
8, -1, - 10 , \ldots
Find the missing 5 terms in the arithmetic sequence which has - 12 as its first term and 24 as its last term:
- 12,\, ⬚,\, ⬚,\, ⬚,\, ⬚,\, ⬚,\, 24
Find the value of x such that x + 2, 6 x + 5, and 9 x + 14 form successive terms in an arithmetic sequence.
Consider the arithmetic sequence: 1.7, \, 2.5, \, 3.3, \, \ldots , \, 12.9
Find d, the common difference.
Solve for n, the number of terms in the sequence.
For each of the following sequences, find the value of n:
0.9, 1.5, 2.1, \ldots where T_n = 22.5
2, 7, 12, \ldots where T_n = 132
The nth term of an arithmetic sequence is T_{n} = - 493.
Find the value of n given that T_{1} = 24 and d = - 11.
The first three terms of an arithmetic sequence are: 46, 39, 32, \ldots
Find the range of values of n for which the terms in the sequence are positive.
Hence, determine the number of positive terms in the sequence.
Find the last positive term in the sequence.
In an arithmetic sequence, T_{5} = 13 and T_{19} = 41.
Find the value of d.
Find the value of a.
Find the 13th term in the sequence.
In an arithmetic sequence, T_{4} = 10.1 and T_{13} = 16.4.
Find the value of d.
Find the value of a.
Find the 29th term in the sequence.
In an arithmetic sequence, T_{7} = 16 and T_{10} = 22.
Find d, the common difference.
Find a, the first term in the sequence.
State the equation for T_{n}.
Find the 30th term in the sequence.
In an arithmetic sequence, the first term is 3.
Find an expression for the 3rd term.
Find an expression for the 10th term.
Given that the 10th term is 4 times the 3rd term, find the common difference d.
In an arithmetic sequence, the 6th term is x and the 14th term is y.
Form an expression for d in terms of x and y.
Form an expression for a in terms of x and y.
Hence, find an expression for the 20th term in terms of x and y.
The first term of an arithmetic sequence is 2. The fifth term is 26.
Find d, the common difference.
Write a recursive rule for T_{n} in terms of T_{n - 1} which defines this sequence and an initial condition for T_{1}.
Consider the arithmetic sequence with terms T_{3} = 14 and T_{12} = 59.
Find d, the common difference.
Find the term T_{1}.
Write a recursive rule for T_{n} in terms of T_{n - 1} which defines this sequence and an initial condition for T_{1}.
The nth term of an arithmetic sequence is given by the equation T_{n} = 12 + 4 \left(n - 1\right).
Complete the table of values.
Calculate the difference between consecutive terms.
| n | 1 | 2 | 3 | 4 | 12 |
|---|---|---|---|---|---|
| T_n |
Plot the points in the table on a number plane.
If the points on the graph were joined, will they form a straight line or an exponential curve?
The nth term of an arithmetic sequence is given by the equation T_{n} = 10 - 10 \left(n - 1\right).
Complete the table of values.
Calculate the difference between consecutive terms.
| n | 1 | 2 | 3 | 4 | 14 |
|---|---|---|---|---|---|
| T_n |
Plot the points in the table on a number plane.
If the points on the graph were joined, will they form a straight line or an exponential curve?
Each of the following table of values represents terms in arithmetic sequence. For each table:
Find d, the common difference.
Write a simplified expression for the general term, T_{n}.
Find the 12th term of the sequence.
| n | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| T_n | 5 | 12 | 19 | 26 |
| n | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| T_n | 3 | \dfrac{24}{5} | \dfrac{33}{5} | \dfrac{42}{5} |
The plotted points represent terms in an arithmetic sequence:
Complete the table of values for the given points:
| n | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| T_{n} |
Find d, the common difference.
Write a simplified expression for the general term, T_{n}.
Find the 15th term of the sequence.
The plotted points represent terms in an arithmetic sequence:
Complete the table of values for the given points:
| n | 1 | 5 | 9 |
|---|---|---|---|
| T_n |
Find d, the common difference.
Write a simplified expression for the general term, T_{n}.
Find the 20th term of the sequence.
The values in the table show terms in an arithmetic sequence for values of n:
Complete the table.
| n | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| T_n | -6 | -26 |
The plotted points represent terms in an arithmetic sequence:
Find d, the common difference.
Write a simplified expression for the general term, T_{n}.
The points are reflected across the horizontal axis to form three new points.
If these new points represent consecutive terms of an arithmetic sequence, write the equation for T_{k}, the kth term in this new sequence.
When a new school first opened, a students started at the school. Each year, the number of students increases by the same amount, d.
At the beginning of its 5th year, it had 393 students. Form an equation for a in terms of d.
At the beginning of the 13th year, the school had 649 students. Form another equation for a in terms of d.
Hence, solve for d, the number of students who joined the school each year.
How many students started at the school when it first opened?
At the beginning of the nth year, the school has reached its capacity at 1097 students. Solve for the value of n.
A diving vessel descends below the surface of the water at a constant rate so that the depth of the vessel after 4 minutes, 8 minutes and 12 minutes is 15 \text{ m}, 30 \text{ m} and 45 \text{ m} respectively.
If n is the number of minutes it takes to reach a depth of 120 \text{ m}, solve for n.
For a fibre-optic cable service, Christa pays a one off amount of \$200 for installation costs and then a monthly fee of \$30.
Complete the table of values for the total cost \left(T\right) of Christa's service over n months.
By how much are consecutive terms in the sequence increasing?
| n | 1 | 2 | 3 | 4 | 18 |
|---|---|---|---|---|---|
| T |
Considering the table of values, plot the points corresponding to n = 1, 2, 3 and 4.
If the points on the graph were joined, would they form a straight line or an exponential curve?
The value of an investment that pays simple interest each year is graphed, where V_n is the value of the investment, in dollars, after n years.
State the value of V_1.
State the value of d, the amount of interest earned each year.
Use the results from the previous parts to write an explicit rule for V_n.
Find the value of the investment after 18 years.
A car bought at the beginning of 2009 is worth \$1500 at the beginning of 2015. The value of the car has depreciated by a constant amount of \$50 each year since it was purchased.
Calculate the purchase price of the car in 2009.
Write an explicit rule for the value of the car after n years.
Solve for the year n at the end of which the car will be worth half the price it was bought for.
A piece of jewellery appreciates in value by a constant amount each year and its value is modelled by the recurrence relation:
V_n = V_{n - 1} + 320, \text{ } V_0 = 2000
where V_n is the value of the jewellery, in dollars, after n years.
State the initial value of the piece of jewellery.
By how much does it appreciate each year?
Write an explicit rule for V_n that gives the value of the piece of jewellery after n years.
What will the investment be worth after 11 years?
A motorbike depreciates in value by a constant amount each year and its value is modelled by the recurrence relation:
V_{n+1} = V_n - 1200, \text{ } V_0 = 15\,000
where V_{n+1} is the value of the motorbike, in dollars, after n+1 years.
State the purchase price of the motorbike.
At what rate is it decreasing in value each year?
Write an explicit rule for V_n that gives the value of the motorbike after n years.
What will the motorbike be worth after 9 years?
The balance of a savings account earning simple interest each year is given by the explicit rule V_n = 2200 + 300 \left(n - 1\right) where V_n is the balance after n years.
How much interest is the account earning each year?
Calculate the account balance after 1 year.
State the original investment amount.
Write a recursive rule for V_{n+1} in terms of V_{n}, and an initial condition V_0.
A mobile phone depreciates in value by a constant amount per month and its value is given by the explicit rule V_n = 1200 - 20 n where V_n is the balance after n months.
By how much does the value of the phone depreciate each month?
What was the purchase price of the phone?
Write a recursive rule for V_{n+1} in terms of V_n , and an initial condition V_0.
Zuber is a taxi service that charges a \$1.50 pick-up fee and \$1.95 per kilometre of travel.
Find the total charge for a 10\text{ km} journey.
Write a recursive rule for T_n in terms of T_{n - 1} which defines the price of a n\text{ km} trip, and an initial condition for T_0.
A rare figurine was purchased for \$60 and ten years later it is worth \$460.
How much did the figurine appreciate by each year if it appreciated in value by a constant amount each year?
Write a recursive rule for V_n in terms of V_{n - 1}, and an initial condition V_0.
Write an explicit rule, V_n, for the value of the figurine after n years.
Find the value of the figurine in another 10 years time.
A piece of machinery depreciated at a constant rate per hour of use. After 140 hours of use, it was worth \$28\,300. After 190 hours of use, it was worth \$28\,050.
Determine the amount of depreciation each hour.
State V_0, the initial value of the machinery.
Write a recursive rule for V_n in terms of V_{n - 1}, and an initial condition V_0.
Write an explicit rule, V_n, for the value of the machinery after n hours of use.
Solve for n, the number of hours of use after which the machinery will be worth a quarter of its original value.
Tabitha is a salesperson and is paid a travel allowance of \$45 for each business trip she takes to demonstrate the use of the product she sells. Each week she is also paid a retainer of \$230.
Calculate the total amount she is paid in a week where she does three business trips.
Write a recursive rule for u_n in terms of u_{n - 1} which defines how much Tabitha is paid in a week where she makes n business trips, and an initial condition for u_0.
Write a recursive rule for v_n in terms of v_{n - 1} which defines how much Tabitha is paid in two week where she makes n business trips, and an initial condition for v_0.
The value of Beirut Bank shares is decreasing by \$2.05 each day. At the beginning of today's trading, the shares are worth \$42.54.
Today is March 8. How much are they worth at the start of March 17?
Write a recursive rule for V_{n+1} in terms of V_n which defines the the value of the shares at the end of day n, and an initial condition for V_0.
Each day, Kumi withdraws \$4 from her bank account to spend on lunch. Before she withdraws this amount on January 1, she has \$2000 in her bank account.
After Kumi withdraws \$4 on January 7, calculate the amount left in her bank account.
How much does Kumi have left in her bank account at the end of February 4?
Write a recursive rule for T_{n} in terms of T_{n - 1} which defines the amount Kumi has in her account at the end of day n, and an initial condition for T_{0}.
When Alison was employed as a project manager, her initial salary was \$50\,000 per annum. After each year of service, she received a salary increase of \$2200.
Write an expression for T_{n}, the value of her salary in her nth year of working.
Calculate her salary in her 15th year of service.