Final answer:
The 11th term of the geometric sequence -3, -6, -12, -24, ... is calculated using the first term and the common ratio. By substituting into the geometric sequence formula, the 11th term is determined to be -3072.
Step-by-step explanation:
The value of the 11th term in the sequence -3, -6, -12, -24, ... can be determined by recognizing the pattern of the sequence. This is a geometric sequence where each term is multiplied by a common ratio to get the next term. In this case, the common ratio is 2 because each term is double the previous one.
- First term (a1) = -3
- Common ratio (r) = 2
- 11th term (an) = a1 × r(n-1) where n is the term number
Substituting the values we have:
an = -3 × 2(11-1)
an = -3 × 210
an = -3 × 1024
an = -3072
The value of the 11th term is therefore -3072.