I have read in a paper explaining spectrum analyzer basic 'When selecting the RBW(resolution BW), there is usually a 1-10 or a 1-3-10 sequence of RBWs available. More RBWs are better because this allows choosing just enough resolution to make the measurement at the fastest possible sweeptime.' Its was also written higher the RBW faster would be the sweep time required. What does these sequences like 1-3, 1-10, 1-3-10 etc in a spectrum analyzer mean?
Notation like "1-3", "1-10", "1-3-10", etc. describes how the range for a particular parameter is varied in steps.
Instruments often cover wide dynamic ranges, over several decades. For example, a voltmeter might cover anywhere from 200 mV to 2000V full-scale, and will have range selections of 200 mV, 2 V, 20 V, 200 V and 2000 V. Each one is 10× the previous one; on a datasheet, this would be described as "1-10" sequence.
With oscilloscopes and spectrum analyzers, such steps are often too coarse, so they sub-divide each decade using a roughly logarithmic scale. If they add one additional step per decade, they use a "1-3" or "1-3-10" sequence. For RBW, it might go 100 Hz, 300 Hz, 1 kHz, 3 kHz, 10 kHz, etc. The ratios between successive steps alternate between 3× and 3.33×. These two ratios are close to each other, creating a rough approximation to a logarithmic scale.
In some cases, you want more choices than that — three steps per decade — so you'll see a "1-2-5" sequence. For example, the horizontal timebase on a scope might go 100 ns, 200 ns, 500 ns, 1 µs, 2 µs, 5 µs, 10 µs, etc. Now the ratios between successive steps follow a pattern of 2×, 2.5× and 2×. Again, these ratios are all similar to each other.