use the sequence: 3, -12, 48, -192, 768.
What are the next 2 terms in the sequence?
Is the sequence arithmetic or geometric?
Write the recursive rule for the sequence.
Write the iterative rule for the sequence.
Thank you!~

Question

use the sequence: 3, -12, 48, -192, 768.
What are the next 2 terms in the sequence?
Is the sequence arithmetic or geometric?
Write the recursive rule for the sequence.
Write the iterative rule for the sequence. 
Thank you!~

thatgingeronfire · Answer

To find the next two terms you have to multiply by -4. So $$768\times-4=-3072$$
$$-3072\times-4=12288$$
An arithmetic sequence goes from one term to the next by always adding (or subtracting) the same value.
A geometric sequence goes from one term to the next by always multiplying (or dividing) by the same value.
So is this arithmetic or geometric?

phenix · Answer

@ThatGingerOnFire It is geometric, so how do you write the recursive and iterative?

thatgingeronfire · Answer

Alright, so to get the recursive you use the formula $$a _{n}=a _{n-1}*r$$
You replace r with the common ratio, which is -4. So it's $$a _{n}=a _{n-1}*-4$$

thatgingeronfire · Answer

That's recursive by the way ^^

thatgingeronfire · Answer

Now for iterative. Iterative for geometric is 
$$a _{n}=a _{1}*r ^{n-1}$$
a1 is the first term of the sequence, so you put in 3 for that. r is the ratio again, so -4. n is just the nth term. So if you wanted to find the 50th term you would put 50 in for the n, but we'll leave it as n. So what's the iterative rule?