Question

Write the formula for the geometric sequence.
7, 21, 63, 189…
A. an=7∙3n-1
B. an=189∙3n-1
C. an=7∙3n
D. an=189∙3n

Answer 1

@tom982

Answer 2

@robtobey

Answer 3

anyone?

Answer 4

What do you think?

Answer 5

d but im guessing

Answer 6

Not quite, let's talk you through this. Taking our sequence:\[7, 21, 63, 189…\] We can see that the common ratio is 3. Now, can you tell me the equation for any geometric sequence?

Answer 7

no i dont know the equation

Answer 8

\[a_n = a_1*r^{n-1}\]

Answer 9

ok now what

Answer 10

So now we need to find a1 and r. a1 is the first term of the sequence, r is the common ratio. Can you tell me what they are?

Answer 11

common ratio i think is 3

Answer 12

no 7

Answer 13

@tom982

Answer 14

Common ratio is 3, because it's getting 3x bigger each time. The first term is 7 because that's what the question gave us. If you put a1=7 and r=3 into my equation above, what do you get?

Answer 15

a or b right

Answer 16

idk im confused thanks for helping me though

Answer 17

this is my last question

Answer 18

It's A, but I'll explain more so you understand.

Answer 19

ok thanks

Answer 20

thanks i got a 100 onthe study guide

Answer 21

All you need to learn is the equation I posted before:

\[a_n = a_1*r^{n-1}\]

To find an expression for the nth term of the sequence, you need a1 and R - that's it! a1 is the first term in the sequence, in this case it's 7. r is the common ratio which is the amount it's being multiplied by each time: 7, 21, 63, 189 is clearly being multiplied by 3 each time. So we put these in:\[a_n = a_1*r^{n-1}\] becomes \[a_n = 7*3^{n-1}\]
Which is your answer :) You can check it by putting n=1, n=2, n=3... in and seeing if it's the same sequence as the one in your question.

Congrats on getting 100!