Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Sequences & Series - Arithmetic - Applied & practical questions.
Test Yourself 1 - Solutions.


 

1. (i)

(ii)

(iii)

2. (i) David has $7,500 and wants to reach $16,000. So he needs to save $8,500.

His saving by month can be summarised as $100, $150, $200, ...So T1 = 100 and d = $50.

We will calculate the sum as his savings accumulate.

(ii) In the 17th month, (using the nth term approach) David would have to be saving
100 + (17 - 1)×50 = $900.

To be saving that amount of post-tax dollars might be very difficult unless David's salary had increased significantly. David might need a Plan B.

3. (i)

(ii)

 

(iii) To decide on the best package, Ellen needs to calculate the other two totals:

So Package 1 has a lower Year 5 salary but a higher total income. Package 2 has however closed the gap and is now higher. Hence by the end of year 7, Package 2 will be better.

So its a matter of what Ellen wants. Before 7 years, she will have completed her studies and have another and better paying position. While at Uni, she needs more income. So she will probably elect Package 1 for the immediate benefits - or at least that is what she told me she would do :-)

4. (i)

 

(ii)

5. In the first year, Damien earns $600 and then $650, $700,...in an arithmetic sequence.

Alyssa earns $500 in the first year and then $570, $640,...

6. (i)

(ii)

7. (i)

(ii)

8. Draw a quick picture.

9. (i) No. of blocks = 180 ÷ 1.5 = 120.

(ii)

(iii)

10. (i) Distance to the 3rd trough and back = 150 m × 2 = 300 m.

OR T3 = 50 + (3-1)50 = 150 m × 2 = 1000 m.

(ii) T10 = 50 + (10 - 1)50 = 500 m one way

Total distance for the last trough = 1,000 m.

(iii)