Question

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 • 3n - 1

an = 7 • (-3)n - 1

an = 7 • 3n

Answer 1

\(\begin{matrix}
\pm 3^{\square}&\pm 3^{\square}&\pm 3^{\square}&\pm 3^{\square}&\pm 3^{\square}\\
\square&-21&\square&\square&567\\
\hline\\
1&2&3&4&5
\end{matrix}\)

Answer 2

so what do you think?

Answer 3

idk

Answer 4

let's try the 2nd term
is -21

based on the given choices, we know the common ratio has something to do with "3"

3 x 7 = 21
-3 x 7 = -21

Answer 5

ok that makes sense so now im left with two options
an = 7 • (-3)n + 1
an = 7 • (-3)n - 1
how do i get the second part?

Answer 6

-21 is the 2nd term
\(\begin{matrix}
-3^\color{red}{1}\\
21\\
\color{red}{2}
\end{matrix}\)

Answer 7

let's see the 5th term
567

\(3^4 = 81\\ 81 \times 7 = 567\\
(-3)^4 = 81\\ 81 \times 7 = 567\\

\begin{matrix}
-3^\color{red}{4}\\
21\\
\color{red}{5th}
\end{matrix}\)

Answer 8

darn, a typo

Answer 9

\(3^4 = 81 \implies 81 \times 7 = 567\\
(-3)^4 = 81\\ 81 \times 7 = 567\\

\begin{matrix}
-3^\color{red}{4}\\
567\\
\color{red}{5th}
\end{matrix}\)

Answer 10

\(\begin{matrix}
(-3)^{\color{red}{0}}&(-3)^{\color{red}{1}}&(-3)^{\color{red}{2}}&(-3)^{\color{red}{3}}&(-3)^{\color{red}{4}}\\
7&-21&\square&\square&567\\
\color{red}{1}st&\color{red}{2}nd&\color{red}{3}rd&\color{red}{4}th&\color{red}{5}th
\end{matrix}\)

Answer 11

so, what do you think?

Answer 12

what do you think would be the 3rd term?

Answer 13

63???

Answer 14

@jdoe0001

Answer 15

\(\begin{matrix}
7(-3)^{\color{red}{0}}&7(-3)^{\color{red}{1}}&7(-3)^{\color{red}{2}}&7(-3)^{\color{red}{3}}&7(-3)^{\color{red}{4}}\\
7&-21&63&\square&567\\
\color{red}{1}st&\color{red}{2}nd&\color{red}{3}rd&\color{red}{4}th&\color{red}{5}th
\end{matrix}\)
yeap

Answer 16

-3*-3 = +9 * 7 = +63
so there, that's the equation :)
\(\bf 7\times (-3)^{n-1}\)