Question

4 what is the common difference or common ratio for the sequence 21, 12, 3, -6, ...? a ( r = \frac{4}{7} ) b ( d = -9 ) c ( r = -9 ) d ( d = \frac{4}{7} )

Explanation:

Step1: Identify sequence type

Check if it's arithmetic (common difference \(d\)) or geometric (common ratio \(r\)). For arithmetic, \(d = a_{n+1}-a_n\) should be constant.

Step2: Calculate differences

\(12 - 21=-9\), \(3 - 12=-9\), \(-6 - 3=-9\). Differences are constant. So it's arithmetic with \(d = -9\).

Answer:

B. \(d=-9\)