Using fission method with a series like v^5 + v^12 + v^19+... I am studying for exam FM and I know we can use the "fission" method to represent a summation like $v^5 + v^{10} + ... + v^{100}$ as $\frac{ \require{enclose}a_{\enclose{actuarial}{100}}}{\require{enclose}s_{\enclose{actuarial}{5}}} $ But what about a series such as $v^5 + v^{12} + v^{19} + ... + v^{54}$? I know you can easily sum this as a geometric series, but I'm just wondering in terms of "symbolic answers" , is there a neat way to represent this? Since if we use the fission method, we only have 5 years before the first payment. For example I know we can write it as $v^5(1 + \frac{1}{{\require{enclose}s_{\enclose{actuarial}{7}}}}\cdot{\require{enclose}a_{\enclose{actuarial}{49}}})$ but this doesn't look that simplified. Thank you in advance!

So, why not write instead $$\frac{1}{v^2}(v^7 + v^{14} + \cdots + v^{56}) = \frac{ \require{enclose}a_{\enclose{actuarial}{56}}}{v^2 \require{enclose}s_{\enclose{actuarial}{7}}}?$$