Final answer:
The explicit formula for the sequence 6, -12, 24, ... is an = an-1 * -2, where a1 = 6 and n is the number of the term.
Step-by-step explanation:
The sequence is defined as 6, -12, 24, ...
To find the explicit formula for the nth term (an), we can observe that each term is obtained by multiplying the previous term by -2. So, the pattern is:
First term: 6
Second term: 6 * -2 = -12
Third term: -12 * -2 = 24
We can generalize this pattern as follows:
an = an-1 * -2
where a1 = 6 and n is the number of the term.
Using this formula, you can find any term in the sequence by plugging in the value of n.