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

Sequences & Series - Geometric - Applied & practical questions.
Test Yourself 1.


 

  1. (i) T1 = 54 and r = 2/3

(ii)

 

(iii)

 

(iv) How many pages would you like to read of this book?

I know your answer - and you are also waiting for the sequel -

The Secret Chamber of the Phoenix Series.
  2. Starting on 1 March 2019, quarterly price rises commence on 1 June, 1 September, 1 December and so on.

(i) 4 January 2020 is in the quarter following the 3rd price rise - so

Toll = 3 × 1.043 = $3.37.

(ii) 4 January 2024 is 4 years after the January 2020 rise - so 16 quarters

Toll = 3 × 1.0419 = $6.32.
  3. (i) T1 = 100 and r = 0.9

So James will be able to sustain the six goldfish after 9 days of carrying water (poor fish).

(ii) Will James ever fill the fish tank?

No that would not be enough effort:). To prove it, use the limiting sum:

So all he could manage would be 1,000 litres.
  4. (i) T1 = 1.5 m and r = 1.02 (the 1 maintains the previous height).

So T5 = 1.5 × 1.024 = 1.62 m.

(ii) "Ever be able" does not imply limiting sum here because Scott cannot keep jumping forever. So find what meet Scott might jump 2 m?

  5. (i)

(ii)

(iii)

Limiting sum 6. (i)

(ii)

 

7. (i)

(ii)