Question

asub n is the number of decimal places in (0.1) to the nth power. Find the first four and eighth terms.

Answer 1

\(a_1= number~ of~ decimal~places ~in~ 0.1^\color{red}{1}, or~\large(\dfrac{1}{10} \large)^\color{red}1,~or~ 0.\color{red}{1} = \color{red}{1}\)
\(a_2= number~ of~ decimal~places ~in~ 0.1^\color{red}2, or~ \large(\dfrac{1}{10} \large)^\color{red}2 , or~ 0.\color{red}{01} = \color{red}2\)
\(a_3= number~ of~ decimal~places ~in~ 0.1^\color{red}3, or~ \large(\dfrac{1}{10} \large)^\color{red}3 , or~ 0.\color{red}{001} = \color{red}3\)

Do you see a pattern?

Answer 2

yes, I got to the decimal 0,1=1 and so forth but when I checked the back of the book it showed 1,2,3, and so on, so how do you get whole numbers from the 0.1, 0.01, ...?

Answer 3

Each number in the sequence is not 0.1, 0.01, 0.001, etc.
To find each number in the sequence, you need to count the number of decimal places in each number above.
Look at my pattern above.
The decimal places themselves are in red, and following that is the number of decimal places.