A contractor hires out machinery. In the first year of hiring out one piece of equipment the profit is £6000, but this diminishes by 5% in successive years. Show that the annual profits from a geometric progression and find the total of all the profit for the first 5 years.
So far I have this…
Profit in the 1st year is £6000
2nd year: £6000-5% = £5700
3rd year: £5700-5% = £5415
I'm unsure how to find out the common ratio of these terms using the general geometric formulas
Sequence : nth term = ar^n-1
Series: Sn= a(r^n -1)/r-1
Best Answer
You are finding the next term by subtracting 5% of the previous term from the previous term, which is equivalent to multiplying the previous term by 95%: $a_{n+1} = a_{n} - 0.05 a_{n} = 0.95 a_{n}$. This should allow you to deduce what the common ratio is.