Question

What are the explicit equation and domain for a geometric sequence with the first term of 5 and a second term of -10?

Answer 1

an=5(-2)^(n-1); all integers when n≥1
an=5(-2)^(n-1); all integers where n≥0
an=5(-15)^(n-1); all integers where n≥1
an=5(-15)^(n-1); all integers where n≥0

Answer 2

@ganeshie8

Answer 3

@phi

Answer 4

@dan815

Answer 5

yay @phi is here

Answer 6

I'm pretty sure the second half is n≥1

Answer 7

right?

Answer 8

You could test each choice. You should get 5, -10 as the first two numbers.

Answer 9

a

Answer 10

wait

Answer 11

b

Answer 12

no a

Answer 13

omg im so confused

Answer 14

***an=5(-2)^(n-1); all integers when n≥1***

for n=1 you get
\[ a_1 = 5(-2)^{1-1} \\ a_1 = 5\cdot (-2)^0 \]
anything to the zero power is 1 , so that simplifies to
\[ a_1= 5 \cdot 1 \\a_1=5\]
that looks good so far

Answer 15

now find a2 for choice A, using n=2

Answer 16

a2=5(-2)^(2-1)
=5(-2)^1
=-10

Answer 17

yes. so choice A looks like the answer.
You could double check the other three, but they won't work (give 5, -10)

Answer 18

ok thank you i have another but i don't know how to post the graphs so oh well

Answer 19

do you know how to take a screen shot?

Answer 20

the wording is horrible

Answer 21

yeah put its on my other computer hang on

Answer 22

It says which logarithmic graph can be used to approximate the value of y in the equation 2^y=3

Answer 23

i don't know how to log that?

Answer 24

take the log of both sides. Log base 2 is the most convenient, but log base 10 or log base 3 (natural log) all can be used.
use the "rule"
\[ \log(a^b) = b \log(a) \]

Answer 25

so… log10 2^y= log10 3

Answer 26

and then use the rule to write
\[ y \log 2 = \log 3 \\ y = \frac{\log 3}{\log 2} \]

Answer 27

to get the answer from a graph, we need to figure out what log base they used.
for example, what is the x value that corresponds to y=1 (that should give us the base)

Answer 28

Here are 3 possible logs
if they gave you log base 2, read off the y value at x=3

Answer 29

thank you i got it