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if-a-n-is-geometric-sequence-and-we-know-p-n-m-2-S-p-f-a-n-a-m-n-m-Attention-The-purpose-of-obtaining-a-relationship-without-the-need-for-direct-calculation-is-the-common-rat




Question Number 199593 by jabarsing last updated on 05/Nov/23
if {a_n } is geometric sequence and     we know , p=((n+m)/2)  ⇒   S_p  = f(a_n ,a_m ,n,m)=?  ■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?
$${if}\:\left\{{a}_{{n}} \right\}\:{is}\:{geometric}\:{sequence}\:{and}\: \\ $$$$ \\ $$$${we}\:{know}\:,\:{p}=\frac{{n}+{m}}{\mathrm{2}}\:\:\Rightarrow \\ $$$$\:{S}_{{p}} \:=\:{f}\left({a}_{{n}} ,{a}_{{m}} ,{n},{m}\right)=? \\ $$$$\blacksquare{Attention}:\: \\ $$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?

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