I'm not getting the correct sum for this geometric progression word problem.

Question

This is another question my teacher asked to do as homework. I've been getting the sum for this word problem.

Here's the word problem:

A man on a diet loses 1.5% of his weight during each week.
(a) If he initially weighs 150kg, write down his body weight at the end of each of the first 5 weeks.
Here's my working out:



(b) How much does he lose in total during that time?
This is the part of the question I've been trying and have been getting the wrong sum. Here's my working out:


The sum for alternate (b) is approximately 727.84kg and it clearly doesn't make sense. I checked the back of the text book where my teacher got this question from and the answer is 10kg. I did the question over and over again and kept coming up with 727.84kg. How do I get 10kg?

Answer 1

You have just added all the terms of the G.P. which is not asked in the question actually the question asks about the decrease in weight i.e. the last term 5^th term in your case.

As per my calculations the fifth term is 139.0824754. If you subtract it from the first term you get 11.

150 - 139.0824754 = 10.91752465 or 11

Method 2(Direct Method):

let X be the weight lost by the person then:

X = a(1-(r)ⁿ)

= 150(1-(0.985)⁵)

=150(1-0.927216502365625)

=150(0.072783497634375)

=10.91752464515625

Answer 2

Just in case you are wondering, you can get 139.0824754 by doing: $$150\times(1-\frac{1.5}{100})^5$$ The 1- bit gets you 0.985, and you can use a this method, a similar method to compound interest, to find the answer of 139.08..... then to get 10.9175 Hope this helped!