Using such expressions is fine, provided you also multiply the annuity factors with the respective probabilities of the life surviving to the start of the second year i.e. probability of the life surviving the first year $$p_x$$.
But there is an easier (slightly more intuitive) way to handle such a stream of expenses:
Suppose there are initial expenses of R100 per policy, and then the regular expenses of R10 starting in the second year, payable annually in advance thereafter. So the R10 is payable at times 1,2,3 ...,n.
This can be treated as initial expenses of R90, plus a stream of R10 payable at time 0,1,2,3,...,n. So you could use a normal annuity factor 10*a[x] (in advance) + 90 to give the expected present value of this stream of expenses.