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38 Videos

Write the first three terms of the sequence. Describe the pattern in words.

`t_n = 3n -2`

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Q1a

Write the first three terms of the sequence. Describe the pattern in words.

```
\displaystyle
f(n) = 4^n + 1
```

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Q1b

Write the first three terms of the sequence. Describe the pattern in words.

```
\displaystyle
t_n = 5n^2 -16
```

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Q1c

Write the first three terms of the sequence. Describe the pattern in words.

```
\displaystyle
f(n) = \frac{n^3}{2}+ 2
```

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Q1d

Write the first three terms of the sequence. Describe the pattern in words.

```
\displaystyle
t_1 =1, t_n = 2t_{n-1} + 5
```

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Q1e

Write the first three terms of the sequence. Describe the pattern in words.

```
\displaystyle
t_1 = -2, t_n = (t_{n-1})^2 -8
```

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Q1f

Graph the first eight terms of each sequence in question 1.

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Q2

The value of a new car bought for $45 000 depreciates at a rate of 15% in the first year and 5% every year after that.

a) Determine the value of the car at the end of the first year, the second year, and the third year. Write these values as a sequence.

b) Determine an explicit formula for the value of the car at the end of year 11.

c) What is the value of the car at the end of year 20? Is this realistic? Explain your thinking.

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Q3

Given the graph, write the sequence of terms and determine a recursion formula using function notation.

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Q4

Write a recursion formula and an explicit formula for each sequence.

5, 7, 9, 11, ....

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Q5a

Write a recursion formula and an explicit formula for each sequence.

2, 4, 16, 256, ...

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Q5b

Investigate the prime—numbered rows of Pascal’s triangle. Describe the property that is common to these rows but not common to the rows that are not prime-numbered.

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Q6

Expand and simplify each binomial.

```
\displaystyle
(2x + 5)^7
```

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Q7a

Expand and simplify each binomial.

```
\displaystyle
(a^2 -3b)^5
```

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Q7b

Expand and simplify each binomial.

```
\displaystyle
(\frac{2}{x} + x^2)^6
```

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Q7c

Expand and simplify each binomial.

```
\displaystyle
(5 - \frac{3}{\sqrt{n}})^4
```

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Q7d

State whether the sequence is arithmetic, geometric, or neither. Determine a defining equation for those that are arithmetic or geometric, and find the 12th term.

`6, 11, 17, 29, ...`

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Q8a

State whether the sequence is arithmetic, geometric, or neither. Determine a defining equation for those that are arithmetic or geometric, and find the 12th term.

`-3, 1, 5, 9, ....`

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Q8b

State whether the sequence is arithmetic, geometric, or neither. Determine a defining equation for those that are arithmetic or geometric, and find the 12th term.

`3, 12, 48, 192, ....`

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Q8c

`2 657 205, -885 735, 295 245, -98415, ....`

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Q8d

The fourth term of an arithmetic sequence is 6 and the seventh term is 27.

Determine the first and second terms.

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Q9

How many terms are in the geometric sequence 7, 21, 63, 3 720 087?

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Q10

A new golf course has 480 lifetime members 3 weeks after it opens and 1005 lifetime members 6 weeks after it opens. Assume the membership m‘crease is arithmetic.

a) Determine the general term that represents the sequence for this situation.

b) How many members were there at the end of the fifth week?

c) When will there be over 2000 members?

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Q11

Determine the sum of the first 10 terms of each series.

`2 + 9 + 16 + 23 + ....`

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Q12a

Determine the sum of the first 10 terms of each series.

`5 -25 + 125 -625 + ....`

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Q12b

Determine the sum of the first 10 terms of each series.

`256 + 128 + 64 + 32 + ....`

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Q12c

Determine the sum of the first 10 terms of each series.

```
- \frac{1}{3} - \frac{5}{6} - \frac{4}{3} - \frac{11}{6} - ...
```

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Q12d

A ball is dropped from a height of 160 cm. Each time it drops, it rebounds to 80% of its previous height.

a) What is the height of the rebound after the 8th bounce?

b) What is the total distance travelled at the time of the 15th bounce?

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Q13

Define each term.

a) principal

b) amount

c) simple interest

d) compound interest

e) annuity

f) present value

g) compounding period

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Q14

Determine the interest earned for each investment.

a) $1000 is invested for 8 months at 5% per year simple interest.

b) $800 is placed into an account that pays 2.5% annual simple interest for 40 weeks.

c) A 90-day $10 000 treasury bill earns simple interest at a rate of 4.8% per year.

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Q15

Alex deposited $500 into an account at 3% simple interest.

a) Write an equation to relate the amount in the account to time.

b) Sketch a graph of this relation for 1 year.

c) How long does it take to earn $10 in interest?

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Q16

Sarah invests $750 in a term deposit, at 4.5% per annum, compounded semi-annually, for 5 years. How much interest will Sarah earn?

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Q17

Abdul decides to invest some money so that he can have $10 000 for a down payment on a new car in 5 years. He is considering two investment options: Account A pays 3.5% per annum, compounded semi-annually. Account B pays 3.2% per annum, compounded monthly.

a) Compare the present values of the two options.

b) Which account is the better choice for Abdul? Explain your reasoning.

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Q18

To save for her university education, Shally will deposit $50 into an account at the end of each month for the next 3 years. She expects the interest rate to be 1.5% per year, compounded monthly, over that time. How much will she have saved after 3 years?

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Q19

Wayne is 16 years old. To become a millionaire by the time he is 50 years old, how much does Wayne need to invest, at the end of every 6 months, at 4% per year, compounded semi-annually?

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Q20

What annual interest rate, compounded monthly, is needed for Eva to accumulate $20 000 by depositing $300 at the end of each month for 5 years?

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Q21

A rental contract calls for a down payment of $1000, and $500 to be paid at the end of each month for 3 years. If interest is at 4.5% per year, compounded monthly, what is the present value of this rental contract?

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Q22

A retirement account contains $100 000. Barb would like to withdraw equal amounts of money at the end of every 3 months for 15 years. If interest is 5% per year, compounded quarterly, what will the size of Barb’s withdrawals be?

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Q23