Question

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -2 and 16, respectively.

Answer 1

\(\large\color{blue}{ a_2=-2}\)
\(\large\color{blue}{ a_5=16}\)

At first to find the ratio, \(\large\color{blue}{ a_n=a_{n-v} \times r^{v}}\) in general, and in your case,

\(\large\color{blue}{ a_5=a_{2} \times r^{5-3}}\)

Answer 2

After that find \(\large\color{blue}{ a_1}\)

then you can fill in the

\(\large\color{black}{ a_n=a_1 \times r^{n-1}}\)

Answer 3

let me know if you need help

Answer 4

how do i find a1?

Answer 5

is the answer an = 1 • (-2)^(n - 1)

Answer 6

-2 would be the second term and 16 would be the 5th term

Answer 7

Have you found the common ratio ?

Answer 8

would it be -8?

Answer 9

do i have to divide by 2?

Answer 10

\(\Large\color{blue}{ a_5 =a_2 \times r^{5-2} }\)

\(\Large\color{blue}{ 16 =(-2)\times r^{5-2} }\)

\(\Large\color{blue}{ -8 = r^{5-2} }\)

\(\Large\color{blue}{ -8 = r^{3} }\)

\(\Large\color{blue}{ (-2)^3 = r^{3} }\)

\(\Large\color{blue}{ r=? }\)

Answer 11

-2

Answer 12

Yes, there we go !

Answer 13

Can you find a1 ?

Answer 14

would it be 1?

Answer 15

Yes !

Answer 16

So you know that
a1=1
r=-2

fill in the equation for any nth term below.

\(\Large\color{blue}{ a_n=a_1\times r^{n-1} }\)

Answer 17

an=1*(-2)^(n-1)

Answer 18

yes

Answer 19

Do you want to type × like me ?

Answer 20

multiplication symbol shortcut , no ?

Answer 21

how?

Answer 22

1) Click and hold ALT

2) click the number code
(using the numbers that are on
the right of the keyboard, and `NOT`
the ones below `F1`, `F2`, `F3`, etc., )

3) release the ALT

number code result
`0 2 1 5 ` ×
`2 4 6 ` ÷
`7 5 4 ` ≥
`7 5 5` ≤
`2 4 1 ` or `7 5 3` ±
`2 4 7` ≈

Answer 23

these is just a small part of it

Answer 24

I'll stop for now

Answer 25

0215

Answer 26

No,

CLICK AND HOLD ALT
CLICK 0 2 1 5 on the number pad on the bottom right corner of your keyboard
RELEASE ALT NOW

Answer 27

oh ×

Answer 28

YEs !

Answer 29

Heh heh

Answer 30

thanks

Answer 31

Anytime:)

Answer 32

°¹²³ counting up to 3

Answer 33

have fun !

Answer 34

do you have time for more?

Answer 35

more questions? I think so :)