Question

Which term of the sequence 2,2√2,4 is128

Answer 1

Answer:

128 is the 13-th term.

Step-by-step explanation:

$\text{The sequence is: } 2,2\sqrt 2,4,... \\ \\ a_n = (\sqrt 2)^{n+1} \\ \\ (\sqrt{2})^{n+1} = 128 \Rightarrow (\sqrt{2})^{n+1} = 2^7\Rightarrow 2^{\frac{n+1}{2}} = 2^7 \Rightarrow\\ \Rightarrow\dfrac{n+1}{2} = 7 \Rightarrow n+1 = 14 \Rightarrow n = 13$