Determine whether the given sequence could be geometric, arithmetic, or neither. If possible, identify the common ratio or difference. 9,\ 13,\ 17,\ 21,\ \cdots

necessaryh

necessaryh

Answered question

2021-08-06

Determine whether the given sequence could be geometric, arithmetic, or neither.
If possible, identify the common ratio or difference.
9, 13, 17, 21, 
a) arithmetic: d=4
b) arithmetic: r=4
c) arithmetic: r=14
d) neither

Answer & Explanation

Derrick

Derrick

Skilled2021-08-07Added 94 answers

Step 1
For a sequence to be arithmetic sequence difference between consecutive terms must be equal.
Mathematically,
d=t2t1=t3t2
Consider the given secuence:
9, 13, 17, 21, 
Step 2
Now check for common difference,
d=139=4
d=1713=4
This proves that,
4=t2t1=t3t2
Therefore, it is a arithmetic progression with common difference 4.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-07-06Added 2605 answers

Answer is given below (on video)

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