Question

Find the 16th term of the geometric sequence 4, -16, 64, ...

Answer 1

Answer:

         $\bold{a_{16} =-4^{16}=-2^{32}=-4\,294\,967\,296}$

Step-by-step explanation:

$a_1=4\\a_2=-16\\a_3=64\\\\\dfrac{a_2}{a_1}=\dfrac{-16}{4}=-4\\\\ \dfrac{a_3}{a_2}=\dfrac{64}{-16}=-4\\\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=-4=r$

The formula:

                     $a_n=a_1\cdot q^{n-1}$

Therefore:

                 $a_{16} =4\cdot(-4)^{16-1}=4\cdot(-4)^{15}=-4^{16}=-2^{32}=-4\,294\,967\,296$