Number Patterns
What are the missing numbers in this sequence?
2, 5, _, 11, _,
8 and 14
State the starting value, t0, of the sequence 20, 19, 18, 17, .
t0=20
For the arithmetic sequences, find the common difference:
5, 11, 17, 23, ...
D=+6
Find the common ratio for the geometric sequence: 6, 30, 150, 750,
Common ratio is 5.
An investment of $5000 is made that pays interest of 4% per annum. How much interest does the investment pay each year?
$200
Describe the behaviour of the sequence:
100, 10, 100, 10, 100
Oscillating
Find the t5 from the sequence: 8, 12, 16, 20, ...
28
Give the next two terms in the arithmetic sequence:
2, 1.5, 1.0, 0.5, ...
0 and -0.5
Find the missing terms in the geometric sequence:
2, __ , 32, 128, __,
8 and 512.
The following recurrence relation can be used to model a simple-interest investment. V0 = 8000, Vn+1 = Vn + 400.
When will the investment reach $12 000 in value?
10 years
Find the next term in the sequence:
243, 81, 27, 9, ...
3
Write down the first five terms of the sequence defined by the following recurrence relation:
P0 = 52, Pn+1 = Pn + 12
52, 64, 76, 88, 100
Fumbles Restaurant had 320 wine glasses. After one week, they only had 305 wine glasses. On average, 15 glasses are broken each week.
Determine how many weeks it takes at that breakage rate for there to be only 200 glasses left?
8 weeks
Find t20 in a geometric sequence that starts at 4 and has a common ratio of 2.
4 194 304.
The following recurrence relation is used to model balance-reducing depreciation on an asset. V0 = 40 000, Vn+1 = 0.9Vn
State the annual percentage depreciation of the asset.
10%
Write down the first five terms of the sequence with a starting value of 5 and the rule ‘multiply each term by 2, and then add 1’
5, 11, 23, 47, 95
Rewrite the following recursion relation in symbolic form, where Vn represents the value after n applications of the rule.
The starting value is 3, and the rule is ‘add 7 to the current term and repeat the process’
V0 = 3, Vn+1 = Vn + 7
Find the missing term in the arithmetic sequence
15, __ , 31, __ , 47,__
23, 39, 55
Generate and graph the first five terms of the sequence defined by the recurrence relation: t0 = 100 tn+1 = 1/10 tn
100, 10, 1, 1/10 , 1/100 .
Simon invests $80 000 with a bank. He will be paid interest at the rate of 6% per year, compounding monthly.
Write a recurrence relation to model Simon’s investment.
V0 = 80 000. Vn+1 = 1.005Vn
Describe how the terms are generated in the number sequence.
1, 9, 25, 49, ...
The squares of odd numbers
State the term name for the term that has a value of 44.
T0 = 20, Tn+1 = Tn + 3
T8 = 44.
Find t40 in an arithmetic sequence that starts at 11 and has a common difference of 8.
331
Find t30 for the following recurrence relation:
t0 = 2000, tn+1 = 0.5tn
0.00000186
The following recurrence relation can be used to model a compound-interest investment:
V0 = 12 000, Vn+1 = 1.08Vn, where Vn is the value of the investment after n years.
Use the rule to find the value of the investment after 4 years, giving your answer to the nearest dollar
V4 = 1.084 × 12 000 = $16 326.