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

Polynomial arithmetic
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

2021-02-03

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,