Question

For the following geometric sequence, determine a1 and r and find an explicit formula for the sequence: 2, -6, 18, -54…
What is a1? a1=2
What is the common ratio r? r= -3
Write an explicit formula for an using the formula for geometric sequences an = a1*(r)^n – 1.
@michele_laino

Answer 1

@whpalmer4

Answer 2

@HELP!!!!

Answer 3

@Michele_Laino

Answer 4

@surjithayer

Answer 5

\[a _{n}=a _{1}r ^{n-1}\]
\[a _{1}=2,r=-3\]
\[a _{n}=2\left( -3 \right)^{n-1}\]

Answer 6

is that my answer?

Answer 7

@18jonea well, does it answer the question? Does it appear to generate the geometric sequence specified in the problem statement?

Answer 8

Yes @whpalmer4

Answer 9

?

Answer 10

If it answers the question and appears to do so correctly, that sounds like a fine answer to me!

Answer 11

ok thank you

Answer 12

I could just tell you "yes, it is correct" but it is more valuable if you understand how to evaluate the answer yourself.

Question asked you to write an explicit formula for the sequence \[2, -6, 18, -54,...\]

You have written an explicit formula that generates
\[a _{n}=2\left( -3 \right)^{n-1}\]\[a_1 = 2(-3)^{1-1} = 2(-3)^0=2*1=2\]\[a_2=2(-3)^{2-1}=2(-3)^1=2*(-3)=-6\]\[a_3=2(-3)^{3-1}=2(-3)^2=2*(9)=18\]\[a_4=2(-3)^{4-1}=2(-3)^3=2*(-27)=-54\]etc.
which matches what you have for a sequence.

Therefore, that's your answer. Nothing there you couldn't have checked out yourself, right?

Answer 13

correct