Why AP & GP should be taught before summation

Today one of my student from SAJC asked me why are there many formulas to memorise for the topic on summation. One of the “formula” on the list was

\sum\limits_{r=1}^{n}{r}=\frac{n}{2}\left( n+1 \right).

I find it difficult to answer this because this is supposed to be a sum of first n terms of arithmetic progression. Students should apply what they learn on AP to evaluate this sum, not memorise it as an object but not knowing what it is.

Most schools will teach AP and GP first before summation as for H2 syllabus, evaluating a summation usually (not always) involves sum of AP, GP or Method of Difference. Just not sure why SAJC chose to be “different”.

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