Answer:
common ratio between successive terms in the sequence is \(\frac{1}{2}\)
Step-by-step explanation:
Common ratio(r) defined as the ratio of a term to the previous term.
also common ratio term is constant.
Given the sequence:
-172 -86 -43 -21.5
⇒\(a_1 = -172\)
\(a_2 = -86\)
\(a_3 = -43\)
\(a_4 = -21.5\)
Then by definition of common ratio:
\(r = \frac{a_2}{a_1}=\frac{a_3}{a_2}=\frac{a_4}{a_3}\)
Substitute the given values we have;
\(r = \frac{-86}{-172} = \frac{-43}{-86}=\frac{-21.5}{-43}\)
⇒\(r = \frac{1}{2}\)
Therefore, the common ratio between successive terms in the sequence is \(\frac{1}{2}\)
