Question

What is a8 for the geometric sequence 6,561;−2,187;729;−243;…6,561;−2,187;729;−243;….

Answer 1

Consider a geometric sequence
`(u_n)`

let
`u_1=a` and the common ratio be r, then the sequence is constructed as follows:


`u_1, u_2, u_3..... = a, ar, a r^(2), a r^(3), ...`

we can observe that each term of the sequence is its previous term * r.


In the given sequence, to find the common ratio we divide 6,561 by −2,187 and get -3. This means that
`r= -(1)/(3)`

Let the first term
`u_1=a=6,561`,

then the eighth term is


`u_8=a* r^(7)= 6,561 (- (1)/(3) )^(7)= -6,561*( (1)/(3) )^(7)= (-6,561)/(2187) =-3`


Answer: -3