Question

what formula describes the following sequence of numbers: (1, -1/3, 1/9, -1/27, 1/81…)

Answer 1

first we need to find if sequence is geometric or arithmetic
\(\large\color{green}{{\rm Geometric~ sequence}}\): when ratio of consecutive terms are the same. to find ratio use this formula \[\large\rm \color{red}{r = \frac{ a_2 }{ a_1 } ~~~or~~ \frac{ a_4 }{ a_3}} \] divide next term by previous one to get r
\(\large\color{green}{{\rm Arithmetic ~sequence }}\) : if the difference between terms are the same
t find common difference \[\large\rm \color{red}{d = a_2 -a_1 ~~~, d=a_4 -a_3}\]