Question

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

Polynomial arithmetic
ANSWERED
asked 2021-08-06
Determine whether the given sequence could be geometric, arithmetic, or neither.
If possible, identify the common ratio or difference.
\(\displaystyle{9},\ {13},\ {17},\ {21},\ \cdots\)
a) arithmetic: \(\displaystyle{d}={4}\)
b) arithmetic: \(\displaystyle{r}={4}\)
c) arithmetic: \(\displaystyle{r}={\frac{{{1}}}{{{4}}}}\)
d) neither

Expert Answers (1)

2021-08-07
Step 1
For a sequence to be arithmetic sequence difference between consecutive terms must be equal.
Mathematically,
\(\displaystyle{d}={t}_{{{2}}}-{t}_{{{1}}}={t}_{{{3}}}-{t}_{{{2}}}\)
Consider the given secuence:
\(\displaystyle{9},\ {13},\ {17},\ {21},\ \cdots\)
Step 2
Now check for common difference,
\(\displaystyle{d}={13}-{9}={4}\)
\(\displaystyle{d}={17}-{13}={4}\)
This proves that,
\(\displaystyle{4}={t}_{{{2}}}-{t}_{{{1}}}={t}_{{{3}}}-{t}_{{{2}}}\)
Therefore, it is a arithmetic progression with common difference 4.
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