Question

good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.

Answer 1

Answer: C. $f(n) = -4(-3)^{n-1}$

Step-by-step explanation: The formula for a geometric sequence is $ar^{n-1}$, where a = first term in the sequence

r = common ratio

n = position of term

Here they already told us a = -4, so we have to figure out r. We can see that in the sequence -4, 12, -36, 108... the terms are being multiplied by -3, which is why the negative and positive terms alternate.

Therefore, the formula is: $f(n) = -4(-3)^{n-1}$

You can try inserting n to check it.

$f(1) = -4(-3)^{1-1} = -4\\f(2) = -4(-3)^{2-1} = 12\\f(3) = -4(-3)^{3-1} = -36\\f(4) = -4(-3)^{4-1} = 108$

Answer 2

Option C

Let's verify

• f(1)=-4(-3)^0=-4
• f(2)=-4(-3)^1=12
• f(3)=-4(-3)^2=-36

Hence verified