This question was on the slight side of confusing, I’ve tried my best to answer it but I feel as if I’ve done it wrong, help would be greatly appreciated!

Question

A model multi-stage rocked it propelled upwards into the air. The first-stage fuel can us bake to propel the rocket upwards by 60cm, the second-stage fuel is able to propel the rocket upwards by 15cm, the third-stage fuel is able to propel the rocket upwards by 3.75cm and so on. Assuming the model rocket has an infinite number of stages (it is super high tech), find the total distance that the multi-stage rocket will travel before all the fuel runs out.

It’s a question on sequences and series, and I’m extremely confused by it :( thank you for the help!

Answer 1

Hi Monica,

This looks like a question on infinite geometric series.

The sum of an infinite geometric series is given by:

S = a/(1-r)

Where S is the sum, a is the first term, and r is the common ratio.

a = 60 (first stage = first term)

r = 0.25

a2/a1 = 15/60 = 0.25

a3/a2 = 3.75/15 = 0.25

S = 60/(1-0.25) = 60/0.75 = 80

The total distance traveled by the multi-stage rocket would be 80 cm.

Hope this helps!