Sagot :
Answer:
64, 128, 256
Step-by-step explanation:
multiply mo lang sa 2 yung last term
GEOMETRIC SEQUENCE
Question:
» What are the next three terms in the geometric sequence 2,4, 8, 16, 32,...
Answer:
- [tex] \sf \large \: {\color{darkblue}{64, \: \: 128, \:}} \footnotesize \: and \: \large \: \: \color{darkblue}{ 256}[/tex]
Solution:
First, we need to determine the common ratio (r).
[tex] \sf{r = \frac{ \: any \: term \: }{ \: preceding \: term \: }} = \frac{ a_{2} }{a_{1} } {\tiny \: \: \: or \: } { \sf \: \: \frac{ a_{3} }{a_{2} }}[/tex]
[tex] \sf r = \frac{4}{2} = \footnotesize \color{brown}{2}[/tex] or [tex] \sf r = \frac{8}{4} = \footnotesize \color{brown}{2}[/tex]
Since r = 2, just multiply 2 to the previous term to obtain next term.
[tex] \sf a_{1} = 2 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf a_{2} = 2 \: (2) = 4 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf a_{3} = 4 \: (2) = 8 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf a_{4} = 8 \: (2) = 16 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf a_{5} = 16 \: (2) = 32 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf a_{6} = 32 \: (2) = \purple{ 64} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf a_{7} = 64 \: (2) = \purple{128} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf a_{8} = 128 \: (2) = \purple{256}[/tex]
Thus, the next three terms in geometric sequence 2, 4, 8, 16, 32,... is 64, 128, and 256.
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