Question

Which formula can be used to find any term ,n ,of the sequence 1,—2/3,4/9,..

Answer 1

`\bf 1~~,~~\stackrel{-(2)/(3)\cdot 1}{-(2)/(3)}~~,~~\stackrel{-(2)/(3)\cdot -(2)/(3)}{(4)/(9)}~~,....`

so, as we can see, it's really multiplying the previous term by -2/3, to get the next term, namely, -2/3 is the common ratio, and of course, the first term is 1.

`\bf n^(th)\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^(n-1)\qquad \begin{cases} n=n^(th)\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ a_1=1\\ r=-(2)/(3) \end{cases} \\\\\\ a_n=1\left( -(2)/(3) \right)^(n-1)\implies a_n=\left( -(2)/(3) \right)^(n-1)`

Answer 2

The answer is A, the answer to the second part is C

Explanation:

:D