How do you write a rule for the nth term of the geometric sequence, then find a6 given 5, -5/3, 5/9, -5/27, ...?

1 Answer
Jim G.
Jun 6, 2017

a_n=5(-1/3)^(n-1)" and " a_6=-5/243

Explanation:

"for the standard geometric sequence"

a,ar,ar^2,...... ,ar^(n-1)larr" nth term"

"where " a=a_1" and r is the common ratio"

r=(a_2)/(a_1)=(a_3)/(a_2)= .... =(a_n)/(a_(n+1))

rArrr=(-5/3)/5=-1/3

rArra_n=ar^(n-1)=5(-1/3)^5larr" nth term rule"

rArra_6=5xx-1/243=-5/243

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