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  1. the answer is (-8,-5)

    step-by-step explanation:

    the endpoint to midpoint is half the length. the length is (-2,-1) so when you are at the midpoint just add it to it to find your answer -6+(-2)= -8 and -4+(-1)=-5 so (-8,-5)

  2. [tex]a_1 = 1[/tex], and

    [tex]a_{n+1} = a_n + (n + 1)[/tex] for [tex]n \ge 1[/tex]

    step-by-step explanation:

    we can analyze the pattern at which the terms increase. let us denote [tex]a_1 = 1[/tex], [tex]a_2 = 3[/tex], [tex]a_3 = 6[/tex], so that we can call

    1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

    note the following:

    from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

    the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

    from [tex]a_1 = 1[/tex], to get to [tex]a_2 = 3[/tex], we add [tex]2(=1+1)[/tex]

    from [tex]a_2 = 3[/tex], to get to [tex]a_3 = 6[/tex], we add [tex]3 (=2+1)[/tex]


    we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

    [tex]a_1 = 1[/tex], and [tex]a_{n+1} = a_n +(n + 1)[/tex] for [tex]n \ge 1[/tex]

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