1. ## geometric sequences

hi all,

Please help me .. I will have a test soon but I still don't know how to use geometric sequences to solve a repeated number. I've posted my question in several forums hoping someone would hlep me .. but .. no .. Thank you so much for helping me!

1. Use the concepts of geometric sequences to write 1.264545454545..... as a rational number in the form a/b where a and b are integers.
How would you solve this using geometric sequence?

2. Write an expression for the apparent nth term of the sequence as a function of n: -2, 1, 6, 13, 22

I noticed that these numbers are increment of 3, but I don't know how I should go about to have the first term as -2 and the rest as positive number

2. $\begin{array}{l}
1.264545 \cdots \\
1 + \frac{{26}}{{100}} + \frac{{45}}{{10000}} + \frac{{45}}{{1000000}} + \cdots \\
1 + \frac{{26}}{{100}} + \sum\limits_{k = 1}^\infty {\frac{{45}}{{10^{2k + 2} }}} \\
\end{array}
$

3. Originally Posted by fallingsky26
hi all,

Please help me .. I will have a test soon but I still don't know how to use geometric sequences to solve a repeated number. I've posted my question in several forums hoping someone would hlep me .. but .. no .. Thank you so much for helping me!

1. Use the concepts of geometric sequences to write 1.264545454545..... as a rational number in the form a/b where a and b are integers.
How would you solve this using geometric sequence?
I will start you off.

$1.26 \overline{45} = 1 + 0.26 \overline{45}$

$= 1 + 0.26 + 0.00 \overline{45}$

$= 1 + \frac {26}{100} + \frac {45}{10^4} + \frac {45}{10^6} + \frac {45}{10^8} + \cdots$

$= 1 + \frac {26}{100} + \frac {45}{10^4} \left( 1 + \frac 1{10^2} + \frac 1{10^4} + \frac 1{10^6} + \cdots \right)$

can you take it from here?

1. Write an expression for the apparent nth term of the sequence as a function of n: -2, 1, 6, 13, 22

I noticed that these numbers are increment of 3, but I don't know how I should go about to have the first term as -2 and the rest as positive number
try to figure out a pattern (they are not all increments of 3)