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I am trying to work out the formula (pretty sure I leant it at some stage, but I can't for the life of me recall it), for calculating the total cost of, for example, 5 cents accruing every month, for 5 years. Eg, the first month is 5c, the second 10c, the 3rd 15c and so on, for 5 years.

Many thanks in advance.

user394139
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1 Answers1

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Hint. One may note that if, for a fixed real number $r$, $$ u_{n+1}=u_n+r,\qquad n=0,1,2\cdots, $$ then

$$ u_n=u_0+n\times r\qquad n=0,1,2\cdots. $$

Then apply it with $r=5$ (cents) and any $u_0$.

Olivier Oloa
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  • OK, thanks for that. Forgive my stupidity, but could you please give me some help applying the formula? I'm struggling with what the u0 represents. – user394139 Nov 29 '16 at 10:48
  • You are welcome. Here $u_0$ can be the initial cost. You are looking for $u_{60}$ ($5$ years=$60$ months), that is $u_{60}=u_0+60 \times 5=u_0+300c$. – Olivier Oloa Nov 29 '16 at 10:50
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    Excellent, many thanks for your kind help. – user394139 Nov 29 '16 at 10:53