this + a noun lets you wrap up everything you just said into one short phrase and make it the starting point of the next sentence, so each sentence opens with what the reader already knows and ends with what is new. That is what keeps a paragraph flowing. Use this for one idea you just gave (this finding, this approach), these for several things you just named (these results), and that to point further back, at something already dealt with (that proposal). All three are neutral and work in any writing.
Pointing back to an idea
this finding /ðɪs ˈfaɪndɪŋ/ — The survey showed a sharp drop in attendance. This finding forced the team to rethink the schedule.
these variables /ðiz ˈvɛriəbəlz/ — The researchers isolated three factors. These variables were then tested one at a time.
that proposal /ðæt prəˈpoʊzəl/ — The board suggested deep budget cuts. That proposal met strong resistance from the staff.
Not ""Attendance fell every term for three years. Attendance falling every term forced a review." (the whole idea is spelled out twice)" — say ""Attendance fell every term for three years. This pattern forced a review." (one phrase packages it, then the sentence moves on)". This pattern wraps up the whole sentence before it, so the next sentence can open with what the reader already knows and save its ending for what is new.
Try it: Which word best joins the two sentences: "The committee flagged several safety risks. ___ risks were later confirmed by an outside audit."? (These / This / It) Answer: These — The first sentence names more than one risk, so the plural 'These' points back to all of them. 'This' would signal a single idea, which doesn't match 'several,' and 'It' is a pronoun that can't sit in front of the noun 'risks.'
Signalling how ideas relate
A connector at the start of a sentence tells the reader what kind of turn is coming. All three here are formal: they belong in essays, reports, and academic writing, not casual chat, where you'd reach for the everyday word instead. furthermore = 'in addition; here is another point in the same direction' (formal; everyday word: also). however = 'in contrast to what I just said' (formal-to-neutral; everyday word: but). subsequently = 'after that; as the next step in time' (formal; everyday phrase: after that). Match the connector to the turn your idea actually takes, they are not interchangeable. Two habits to keep: however can also sit after the subject (The plan, however, collapsed), and one connector per turn is enough, a connector on every sentence makes writing harder to follow, not easier.
furthermore /ˈfɜrðərˌmɔr/ — The early trials were promising. Furthermore, later studies confirmed the same effect.
however /haʊˈɛvər/ — The plan looked solid on paper. However, it collapsed once real costs came in.
subsequently /ˈsʌbsəkwəntli/ — The team finished the research phase. Subsequently, they began drafting the report.
Not ""The method was accurate. Furthermore, it was far too slow to use." (furthermore signals you're adding support, but a drawback is a contrast)" — say ""The method was accurate. However, it was far too slow to use." (however correctly flags the contrast)". Pick the connector that matches your turn: furthermore only when you add weight in the same direction, however for a contrast, subsequently for the next step in time. The wrong one sends the reader the wrong signal.
Try it: Which connector fits: "The first method reduced errors by half. ___, it was too slow for daily use."? (However / Furthermore / Subsequently) Answer: However — The second sentence contradicts the good news in the first, so 'However' signals that contrast. 'Furthermore' would add another point in the same direction, and 'Subsequently' would mark a next step in time, neither of which matches a drawback.
Try it: Which connector fits: "The committee approved the budget in March. ___, funds were released to each department."? (Subsequently / However / Furthermore) Answer: Subsequently — The release of funds is the next event in a sequence, so 'Subsequently' marks that time order. 'However' would wrongly signal a contrast, and 'Furthermore' would add a parallel point rather than show what happened next.