Question

Find the ${10}^{th}$ term of the sequence defined by a $a_n=(-1{)}^{2n-1}{.5}^n$

Answer 1

$a_n=(-1{)}^{(2n-1)}{5}^n$

$a_{10}=(-1{)}^{2\left(10\right)-1}{5}^{10}$

$=(-1{)}^{19}{5}^{10}$

$a_{10}=-5^{10}$