write a rule for the sequence and list the next term
rule:_____
-6,-24,96,384,____
alternate signs as in -,-,+,+,-,-,+,+,...
and just keep multiplying by 4
a_n = (-1)^(1+[(n-1)/2] * 6 * 4^(n-1)
where [x] is the greatest integer (floor) function
The rule for the sequence is multiplying each term by -4.
Next term: -6 x -4 = 24
To find the rule for the sequence and determine the next term, we can observe the pattern in the given numbers.
From -6 to -24, each term is being multiplied by -4. (-6 * -4 = 24)
From -24 to 96, each term is being multiplied by -4 as well. (-24 * -4 = 96)
From 96 to 384, each term is being multiplied by -4. (96 * -4 = -384)
Therefore, the rule for the sequence is to multiply each term by -4.
To find the next term, we'll apply the rule to the last term in the sequence:
384 * -4 = -1536
So, the next term in the sequence is -1536.