Question
uestion etermine if the sequence below is arithmetic or geometric and determine the common tifference / ratio in simplest form. 125,25,5,ldots Answer Attemperout of? This is square sequence and the square is equal to square
Solution
4.7
(152 Votes)
Chloe
Elite ยท Tutor for 8 years
Answer
### This is a geometric sequence and the common ratio is equal to
.
Explanation
## Step 1: Check for Arithmetic Sequence### An arithmetic sequence has a constant difference between consecutive terms. The difference between 25 and 125 is
. The difference between 5 and 25 is
. Since the differences are not the same, this is not an arithmetic sequence.## Step 2: Check for Geometric Sequence### A geometric sequence has a constant ratio between consecutive terms. The ratio between 25 and 125 is
. The ratio between 5 and 25 is
. Since the ratios are the same, this is a geometric sequence.## Step 3: Determine the Common Ratio### The common ratio is the constant multiplier between consecutive terms, which we found to be
.