Given the geometric sequence: 9, 3, 1, ... . Find S6

Question

 Given the geometric sequence: 9, 3, 1, ... . Find S6 

Answer 1

Geometric sequencing is like figuring out a puzzle...

Ask yourself:  What did I do to get from 9 to 3, then from 3 to 1?

The answer is you divided by 3.  Geometric sequencing is a multiplication sequence, so therefore you are actually multiplying each new answer by 1/3

 

The sequencing formula is:   t _n=ab

 

t_n= 9(1/3) --- The 9 & 1/3 are the substitutions for a & b

t₁₌  9                            First term

t₂₌ 9(1/3)= 3                Second term

t₃₌ 3(1/3)= 1                Third term

t₄= 1(1/3)= 1/3             Fourth term

t₅₌ 1/3(1/3) = 1/9         Fifth term

t₆= 1/9 (1/3) = 1/27      Sixth term

 

I hope this helps.