Question

Determine whether the given sequence could be geometric,arithmetic, or neither.
If possoble, identify the common ratio or difference.
9, 13, 17, 21, ....
a. arithmetic \(d = 4\)
b. geometric \(r = 4\)
c. geometric \(r = \frac{1}{4}\)
d. neither

Answer 1

Step 1 Fora sequence to be arithmetic sequence difference between consecutive terms must be equal.
Mathematically,
\(d=t_{2}-t_{1}=t_{3}-t_{2}\)
Consider the given sequence: 9,13,17,21,...
Step 2
Now check for common difference,
\(d = 13 - 9 = 4\)
\(d = 17 - 13 = 4\)
This proves that,
\(4 = t_{2} - t_{1} = t_{3} -t_{2}\)
Therefore, it is arithmetic progression with common difference 4,