Question

Find an equation for the nth term of the sequence.

-3, -12, -48, -192, ...

an = 4 • -3n + 1
an = -3 • 4n - 1
an = -3 • 4n
an = 4 • -3n

Answer 1

@yanasidlinskiy

Answer 2

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 • 3n - 1
an = 7 • (-3)n - 1
an = 7 • 3n

Answer 3

@yanasidlinskiy

Answer 4

\[a _{n}=ar ^{n-1}\]
a=first term
r=common ratio

Answer 5

\[r=\frac{ a _{2} }{ a _{1} }=\frac{ -12 }{ -3 }=4\]
a=-3
\[a _{n}=-3*4^{n-1}\]

Answer 6

for second
\[a _{n}=ar ^{n-1}\]
\[a _{2}=ar ^{2-1}=ar=-21 ...(1)\]
\[a _{5}=ar ^{5-1}=ar^4=567 ...(2)\]
divide (2) by (1)
\[\frac{ ar^4 }{ ar }=\frac{ 567 }{ -21 }\]
\[r^3=-27,r=-3\]
from (1)
a=7
\[a _{n}=?\]