1st way
To solve this we need to know ratio.
[tex] - \frac{1}{5} \div \frac{1}{5} = - 1 \\ [/tex]
Now we can see that odd numbers of geometric sequence are positive and even numbers are negative. 91 - odd number, so it will be positive. If ratio is equal to -1, than 91st number is
[tex] \frac{1}{5} \\ [/tex]
2nd way
Firstly, we need to find ratio.
[tex]- \frac{1}{5} \div \frac{1}{5} = - 1 \\ [/tex]
Secondly, we need to use this formula
[tex]b_n=b_1 \times q^{n-1} \\ [/tex]
[tex]b_{91}= \frac{1}{5} \times ( - 1)^{91-1} = \frac{1}{5} \\ [/tex]
