Answer
The quotient of every consecutive terms is the same or constant.
(Proved below.)
Work Step by Step
The sum of an arithmetic sequence is given by: $S_n=\dfrac{n}{2}[a_1+a_n]$ and the nth term for an arithmetic sequence is given by $a_n=a_1+(n-1) d$
We are given that $1,-2, 4,-8, 16.....$
Here, $\dfrac{a_2}{a_1}=\dfrac{-2}{1}=-2 ; \\\dfrac{a_3}{a_2}=\dfrac{4}{-2}=-2 \\ \dfrac{a_4}{a_3}=\dfrac{-8}{4}=-2 \\\dfrac{a_5}{a_4}=\dfrac{16}{-8}=-2$
It has been noticed that the quotient of every consecutive term is the same or constant .
Hence, the result has been proved.
