We use the third catalog of blazars detected by Fermi/LAT (3LAC) and gamma-ray narrow-line Seyfert 1 Galaxies (gamma-NLSy1s) to study the blazar sequence and relationship between them. Our results are as follows. (i) There is a weak anticorrelation between synchrotron peak frequency and peak luminosity for both Fermi blazars and gamma-NLSy1s, which supports the blazar sequence. However, after Doppler correction, the inverse correlation disappeared, which suggests that anticorrelation between synchrotron peak frequency and peak luminosity is affected by the beaming effect. (ii) There is a significant anticorrelation between jet kinetic power and synchrotron peak frequency for both Fermi blazars and gamma-NLSy1s, which suggests that the gamma-NLSy1s could fit well into the original blazar sequence. (iii) According to previous work, the relationship between synchrotron peak frequency and synchrotron curvature can be explained by statistical or stochastic acceleration mechanisms. There are significant correlations between synchrotron peak frequency and synchrotron curvature for whole sample, Fermi blazars and BL Lac objects, respectively. The slopes of the correlation are consistent with statistical acceleration. For FSRQs, LBLs, IBLs, HBLs, and gamma-NLS1s, we also find a significant correlation, but in these cases the slopes cannot be explained by previous theoretical models. (iv) The slope of the relation between synchrotron peak frequency and synchrotron curvature in gamma-NLS1s is larger than that of FSRQs and BL Lac objects. This result may imply that the cooling dominates over the acceleration process for FSRQs and BL Lac objects, while gamma-NLS1s is the opposite.