ANSWER: 1st option, the red giant star.
EXPLANATION: (a)The main stages of a star, one after another is,
giant cloud of gas(at the very first stage, stars are just the low-temperature gas cloud, gas molecules can not be formed by such low temperature), protostar(in this stage a good amount of heat energy is produced by a baby star), T-tauri phase, Main sequence, Red giant, Heavy elements fusion, supernovae and planetary nebula.
(b) The 2nd option, horizontal branch phase is not correct. Because for intermediate stars like Sun, this stage comes just after the red giant stage. In this stage, energy released from helium fusion at core and hydrogen fusion in shell surrounding the core.
(c) From option a, above, we come to know that protostar is the next stage of giant cloud of gas, so option 3 is not correct.
(d)And the last option is indicating to the last stage of a star.And the periode of this stage can be of trillions of years.
The next stage in a star's life after the main-sequence phase is the red giant phase....
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