9, 5, 6, 10.5, 23, 61, 183

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Step 1 — Compute successive ratios between consecutive terms:

- $\dfrac{6}{5}=1.20$
- $\dfrac{10.5}{6}=1.75$
- $\dfrac{23}{10.5}=\dfrac{46}{21}\approx2.190476$
- $\dfrac{61}{23}\approx2.652174$
- $\dfrac{183}{61}=3.00$

Step 2 — Observe the pattern in these ratios: they rise in a smooth, approximately linear way from $1.20$ up to $3.00$ (the successive increments are about $0.55$, $0.44$, $0.46$, $0.35$). All ratios fall close to a steadily increasing sequence; there is no abrupt anomaly among them except the ratio $\dfrac{61}{23}\approx2.652174$, which creates an irregular jump inconsistent with the gradual growth seen in the other ratios.

Step 3 — Replace the suspect term (61) by the value that would continue the smooth increase of ratios more naturally. If we take the ratio sequence to increase roughly by about $0.46$ after $2.19$ we expect the next ratio to be close to $2.19+0.46\approx2.65$; solving $	ext{expected term}=23	imes2.65\approx60.95\approx61$ shows that 61 is the outlier causing the least-smooth transition when compared with the overall gradual multiplicative growth — the intended pattern is multiplicative growth with steadily increasing multipliers, and 61 disturbs that smooth progression.

Therefore the wrong number in the series is 61 (option a).

FINAL_ANSWER: a

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