Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.

Answer 1

@freckles

Answer 2

@sweetburger

Answer 3

@Jaynator495

Answer 4

@iambatman

Answer 5

@ikram002p

Answer 6

explicit formula \[\huge\rm a_n = a_1 * r^{n-1}\]
where a_1 is first term
r =common ratio
n=term

Answer 7

for this question we have to find
common ratio
and first term with given 2nd and 5th
\[\large\rm a_2 = -6~,~~~~~~~~~~~~a_5 = 162\]
a_2 means 2nd term so when a_2 =-6 n =2
when a_5 = 162 n =5
n here represent the number of terms
so we should write two equations
\[\huge\rm a_\color{Red}{2 }= a_1 * r^{\color{red}{n}-1}\]
a_2 = -6 so i'll replace a_2 with -6
n =2 bec it's a 2nd term \[\huge\rm \color{Red}{-6 }= a_1 * r^{\color{red}{2}-1}\]
now write 2nd equation when n=5 a_5 =162

Answer 8

do you understand ?:=))

Answer 9

could the answer be between these two?

Answer 10

i don't yet
do you understand what i said above ?

Answer 11

know*

Answer 12

\[\huge\rm a_n = a_1 * r^{n-1}\]
write 2nd equation
when n= 5 and a_5 = 162
just like i did for a_2

Answer 13

162 = a_1 * r^5-1

Answer 14

right 5-1 =4
so it would be
\[\huge\rm \color{Red}{162 }= a_1 * r^{\color{red}{5}-1}\]
\[\huge\rm \color{Red}{-6 }= a_1 * r^{\color{red}{2}-1}\]

first equation
\[\large\rm \color{Red}{162 }= a_1 * r^{\color{red}{4}}\]
2nd equation
\[\large\rm \color{Red}{-6 }= a_1 * r^{\color{red}{1}}\]
i remembered when we solved arithmetic where we subtracted both equation
but here we should divide them