Question Number 199593 by jabarsing last updated on 05/Nov/23
$${if}\:\left\{{a}_{{n}} \right\}\:{is}\:{geometric}\:{sequence}\:{and}\: \\ $$$$ \\ $$$${we}\:{know}\:,\:{p}=\frac{{n}+{m}}{\mathrm{2}}\:\:\Rightarrow \\ $$$$\:{S}_{{p}} \:=\:{f}\left({a}_{{n}} ,{a}_{{m}} ,{n},{m}\right)=? \\ $$$$\blacksquare{Attention}:\: \\ $$The purpose of obtaining a relationship without the need for direct calculation is the common ratio of the sequence. For example, in a geometric sequence with a negative common ratio, if the sixth and tenth terms are equal to 5 and 12, the sum of the first 7 terms of this sequence?