Answer
$2.67\%$
Work Step by Step
Annual growth rates (years 1→10):
5%, 3%, 4%, −1%, −2%, 2%, 3%, 4%, 6%, 3%.
Compute trend as the geometric mean of the growth factors:
Growth factors = 1.05, 1.03, 1.04, 0.99, 0.98, 1.02, 1.03, 1.04, 1.06, 1.03.
Product of factors ≈ 1.3017721.
The yearly rate: $\sqrt[10]{1.3017721}− 1\approx 0.0267=2.67\%$
Expansionary phase — the contiguous years that most clearly show above-trend growth are years 7–9 (3%, 4%, 6%), which average about 4.33% and include the largest positive run.
Recessionary phase — the clearest recessionary run is years 4–5 (−1%, −2%), a consecutive fall below zero (and well below the 2.67% trend).
(Alternatively, years 1–3 (5%, 3%, 4%) also show sustained above-trend growth, but years 7–9 contain the single strongest year (6%) within a short expansionary run. The recession is unambiguously years 4–5.)
