Answer:
[tex]2048[/tex], assuming that [tex]128[/tex] comes right after [tex]8[/tex] in the sequence.
Step-by-step explanation:
In a geometric sequence, the ratio between any two consecutive items of the sequence should be the same.
Assuming that the term [tex]128[/tex] comes right after [tex]8[/tex]. The ratio between the two would be [tex](128 / 8) = 16[/tex].
Likewise, if the term right after [tex]128[/tex] is [tex]x[/tex], then the ratio [tex](x / 128)[/tex] should also be equal to [tex]16[/tex]. Hence:
[tex]\displaystyle \frac{x}{128} = 16[/tex].
[tex]\displaystyle x = 16 \times 128 = 2048[/tex].
In other words, under the assumptions, [tex]2048[/tex] would be the term that follows [tex]128[/tex].
Answer:
256
Step-by-step explanation:
Note that
8 = 2³ and 128 = [tex]2^{7}[/tex]
The term that follows 128 is then
[tex]2^{8}[/tex] = 256
These are the terms of a geometric sequence with
common ratio r = 2
8 is the third term
128 is the seventh term
256 is the eighth term
