Answer:
Step-by-step explanation:
this the gemetric sequence because : -12/6 =24/-12=-48/24=-2 (common rat)
the sum is : S= u1 ×(d^n - 1)(d-1)
d = -2 u1 = 6 S= -2046
6((-2)^n -1) /(-2 -1) = -2046
(-2)^n -1 =1023
(-2)^n = 1024 but 1024 = 2^10 = (-2)^10
so : (-2)^n = (-2)^10
n=10 conclusion : 10 terms
The number of terms of the sequence is 10.
A geometric sequence exists a sequence of numbers where each term after the first term exists found by multiplying the earlier one by a fixed non-zero number, named the common ratio.
The terms of the sequence 6, -12, 24, -48, ...
Sum = -2046
Geometric sequence:
-12/6 = 24/-12 = -48/24 = -2
Sum of terms:
[tex]$S = u_{1} *(d^n - 1)(d-1)[/tex]
Let, d = -2, [tex]u_{1} = 6[/tex] and S = -2046
[tex]6((-2)^n -1) /(-2 -1) = -2046[/tex]
[tex](-2)^n -1 =1023[/tex]
[tex](-2)^n = 1024[/tex]
But the number of terms = 10
[tex]1024 = 2^{10} = (-2)^{10}[/tex]
so,[tex](-2)^{n} = (-2)^{10}[/tex]
Therefore, the correct answer is 10.
To learn more about geometric sequence
https://brainly.com/question/1729067
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