What is the next stage in a star's life after the main-sequence phase?
After the main sequence stage in which a Star burn it's Hydrogen into Helium, the Star rearranges it self expanding it's outer layers and shrinking its core becoming a Red-Giant.
In the Red-Giant stage the Star is dense enough to burn Helium into Carbon, as fusing Helium to Carbon requires a triple fusion reaction as Helium first fuses to form Beryllium and Beryllium is very Unstable so this would require the Star to be dense enough to support enough reactions till the formation of Carbon.
It is estimated that the radius of the Sun as a Red-Giant will be about 2 AU compared to it's Radius of 0.1 AU in the main sequence Stage.
1 AU = 149 Million km