MHB Find the 18th term in the sequence:

[karush]

Find the $18th$ term in the sequence:

$$\frac{1}{2},1,2 $$
$$a_1= \frac{1}{2}\ \ \ \ n=18\ \ \ \ r=2 $$
$$a_n=a_1\cdot r^{n-1}=131072$$

 

[MarkFL]

I'm thinking:

$$a_n=2^{n-2}$$

And so:

$$a_{18}=2^{16}=65536$$

 

[karush]

$$a_n=a_1 \cdot r^{n-1}$$

was the eq in the book unless the ratio is wrong

 

[suluclac]

$$a_n=\frac{1}{2}\cdot 2^{n-1}=\frac{2^{n-1}}{2}=2^{(n-1)-1}=2^{n-2}$$

 

[MarkFL]

$$a_n=a_1 \cdot r^{n-1}$$

was the eq in the book unless the ratio is wrong

No, that is correct...I just simplified:

$$a_n=a_1r^{n-1}=2^{-1}\cdot2^{n-1}=2^{n-2}$$

 

[karush]

ok got it..