find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively. an = 7 • (-3)n^( + 1) an = 7 • 3^(n - 1) an = 7 • (-3)^(n - 1) an = 7 • 3^n

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find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively. an = 7 • (-3)n^( + 1) an = 7 • 3^(n - 1) an = 7 • (-3)^(n - 1) an = 7 • 3^n

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\[a _{n}=ar ^{n-1^{}}\] \[find~a _{2}~and~a _{5}\] and divide
let a be the first term find a2 and a5

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\[a _{2}=ar ^{2-1}=ar=-21\] \[a _{5}=ar ^{5-1}=ar^4=567\] divide \[\frac{ ar^4 }{ ar }=\frac{ 567 }{ -21 },r^3=-27=\left( -3 \right)^3,r=-3\] ar=-21 find a
can you find?
\[\frac{ ar }{ r }=\frac{ -21 }{ -3 }=?\] then write an=?
if 2nd term is negative and 5th term is positive, then the common ratio is obviously negative. ((There is no other way for such geom. sequence))
@SolomonZelman its c right?
yes, it's C.

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